THESIS REPORT, EUROPEAN WIND ENERGY MASTER PROGRAM, ELECTRIC POWER SYSTEM TRACK

Harmonic Analysis of Collection Grid in

Offshore Wind Installation

By Chan Shan

For obtaining the degree of Master of Science in

Electrical Engineering at Delft University of Technology (TU Delft)

& Wind Energy at Norwegian University of Science and Technology (NTNU)

Supervisors: Prof. Ole-Morten Midtgård (NTNU)

Dr. ir Jose Rueda Torres (TU Delft)

Acknowledgements

The research work of this thesis has been carried out as part of European Wind Energy Master

（EWEM）program hosted by Delft University of Technology (TU Delft) and in cooperation

with Norwegian University of Science and Technology (NTNU). I would like to extend my

sincere gratitude to all those who encouraged me and supported me throughout the period of

working on my thesis.

My deepest gratitude goes first to my supervisor Prof. Ole-Morten Midtgård from NTNU,

for offering me the chance to start this graduation thesis and for his patient help, guidance and

encouragements. And also many thanks to my daily supervisor Salvatore D'Arco at SINTEF

Energy Research, his suggestions and guidance helped me a lot. Thank you for introducing

me to the world of offshore wind energy generation.

Special gratitude to my supervisor Dr. José L. Rueda from TU Delft, for your patience and

encouragement when I met difficulties, for giving me precious advice on my thesis.

I also want to thank all the persons who helped me all along the time of my thesis. Especially

in the one-year extension of graduation, I have been on sick leave for over half year suffered

from depression. All the responsible officers and professors in EWEM program contacted

with me are so kindly to offer their encouragement and patient help to me. I really appreciate

your responsible attitude and warm heart.

In addition, I want to express thanks to my boyfriend Yi. He gave me so much love and

encouragement during this year.

Last but not the least, my gratitude also extends to my family for their endless love, caring for

me all the time and giving me the chance to study in Europe and never being disappointed on

me.

Chan Shan

Oct 10, 2017

Abstract

Wind power as a green and low-carbon renewable energy could effectively mitigate

the energy crisis and reduce environmental pollution, including the rapid developing

offshore wind power with its rich reserves, wind stability, high wind speed, less

interference, noise and other advantages. The trend for development of offshore wind

farms is towards a growing size of installed power. This together with higher

distances from the shore leads in many cases to HVDC connection as a preferred

choice for power export. Thus, the wind turbines are connected through a collection

grid to an offshore platform. As the offshore wind farm contains a large number of

power electronic devices and submarine cables, it will inevitably lead to the

occurrence of harmonic resonance. Offshore wind farm harmonic and resonance will

affect the power quality, while poses a huge challenge to the power grid and wind

power.

In this thesis work, a comprehensive harmonic analysis in offshore wind farm was

studied. Firstly, a detail configuration of the wind energy conversion system and

harmonic analysis basics are described and interpreted. Next, a suitable model of one

offshore wind farm is built and validated in Matlab/Simulink. The equivalent circuit is

calculated for the components in the aggregated wind farm based on their harmonic

model. And potential resonance problems are analyzed by frequency scan method to

calculate the resonance impedance and frequency. Afterwards, based on the self-built

system model, potential harmonic issues that arise in the system are investigated in

time domain to interpret the THD at PCC between the collection grid and the onshore

grid. As well, a few effective strategy for suppressing harmonics are simulated to

evaluate the various influence on the harmonic issue. Both the designed C-type filter

and active power filter performed a satisfying results on harmonics suppression. The

main contents are as follows:

1) Study on the basics of harmonics and discuss the potential sources and the

mechanism of harmonic resonance in offshore wind farms. The simulation model

of PMSG Wind Energy Generation System is established. Harmonic

characteristics of machine-side converter, grid-side converter and line filter

capacitor are analyzed. It could be deducted that machine-side converter current is

mainly influenced by wind speed and mechanical control system. Grid-side

current, which has a lower harmonic to the machine-side current, are mainly

affected by PWM control system of converter. Thus, harmonic current injected

from PMSG to grid is mainly determined by gird side converter and filter in wind

turbine out port.

2) System resonance problem of OWF was analyzed in equivalent circuit models.

And then the frequency scan method is applied to detect the influence components

which potentially affect the harmonic resonance. From the simulation results, the

main resonance points are similar at collection grid bus of wind farm in HVAC

transmission system and HVDC transmission system, which are around 7th order

frequency. Resonance points are also influenced by length, inductance and

capacitance of submarine cable, due to the high distributed capacitance of

submarine cable.

3) Study on the strategy for suppressing harmonics at an offshore wind farm. The

harmonics distribution in cases with C-type filter or active power filter adopted

are designed and analyzed in the simulation models. The C-type passive filter

performed satisfying results on harmonics suppression.

Keywords

Offshore wind farm; PMSG; HVDC transmission; harmonic and resonance analysis;

impedance scan method; filter

Contents

Acknowledgements ........................................................................................................................... 2

Abstract ............................................................................................................................................. 3

Keywords ........................................................................................................................................... 4

Chapter 1 Introduction .................................................................................................................... 10

1.1 Background and Motivation .............................................................................................. 10

1.2 Problem Description .......................................................................................................... 11

1.3 Objective and Scope .......................................................................................................... 12

1.4 Report Layout .................................................................................................................... 12

Chapter 2 Basic of Harmonics ......................................................................................................... 14

2.1 The Definition of Harmonic ............................................................................................... 14

2.2 Total Harmonic Distortion (THD) ....................................................................................... 14

2.3 Fast Fourier Transform (FFT) ............................................................................................. 15

2.4 Sources of Harmonics in Offshore Wind Farms ................................................................. 16

2.5 Harmonic Resonance ........................................................................................................ 17

2.5.1 Introduction ........................................................................................................... 17

2.5.2 Parallel Resonance ................................................................................................. 17

2.5.3 Series Resonance .................................................................................................... 18

2.6 Harmonic Analysis Methods ............................................................................................. 19

2.6.1 Introduction ........................................................................................................... 19

2.6.2 Frequency Scan Method ........................................................................................ 19

2.6.3 Time-Domain Harmonics Analysis .......................................................................... 20

2.7 Summary ........................................................................................................................... 20

Chapter 3 Basics of Offshore Wind Farm System ........................................................................... 22

3. 1 Wind Turbine Fundamentals ............................................................................................ 22

3.1.1 Wind Turbine Characteristics ................................................................................. 22

3.1.2 Operation Modes of Wind Turbine ........................................................................ 23

3.1.3 Category of Wind Turbine Generators ................................................................... 24

3.2 Collection Grid in Offshore Wind Farm ............................................................................. 27

3.2.1 Collection Grid Topology ........................................................................................ 27

3.2.2 MVAC/MVDC collection grid .................................................................................. 29

3.3 Transmission System to Shore ........................................................................................... 30

3.3.1 Introduction ........................................................................................................... 30

3.3.2 HVAC Transmission ................................................................................................. 30

3.3.3 LCC-HVDC Transmission ......................................................................................... 31

3.3.4 VSC-HVDC Transmission ......................................................................................... 32

3.3.5 Transmission System Selection ............................................................................... 33

Chapter 4 Modelling and Harmonic Analysis in Offshore Wind Farm ............................................. 34

4.1 Wind Energy Generation System ....................................................................................... 34

4.1.1 Introduction ........................................................................................................... 34

4.1.2 Parameter Setting of Wind Turbine ........................................................................ 34

4.1.3 Model Simulation Results ....................................................................................... 35

4.1.4 Summary ................................................................................................................ 39

4.2 Offshore Wind Farm System ............................................................................................. 40

4.2.1 System Description ................................................................................................. 40

4.2.2 Simulation Validation of the OWF case .................................................................. 42

4.2.3 Simulation Results and Analysis of Harmonic Output Characteristics ................... 43

4.3 Summary ........................................................................................................................... 44

Chapter 5 Harmonic Resonance Analysis in OWF ........................................................................... 46

5.1 Introduction ...................................................................................................................... 46

5.2 Theory of Harmonic Models ............................................................................................. 46

5.2.1 Harmonic Model of PMSG with full scale converter .............................................. 46

5.2.2 Harmonic Model of Transformer ............................................................................ 49

5.2.3 Harmonic Model of Subsea Cables ........................................................................ 50

5.2.4 Harmonic Model of VSC- HVDC system .................................................................. 51

5.3 Developing the Equivalent Harmonic Model of the OWF ................................................. 54

5.4 Results and Harmonic Resonance Analysis ....................................................................... 56

5.4.1 The Influence of Transmission System on Harmonic Resonance in OWF .............. 57

5.4.2 The Influence of Cable on Harmonic Resonance in OWF ....................................... 58

5.5 Summary ........................................................................................................................... 62

Chapter 6 Filter Design for Suppressing Harmonics in OWF ........................................................... 63

6.1 Introduction ...................................................................................................................... 63

6.2 Passive Filter ...................................................................................................................... 63

6.2.1 Fundamental of passive filter ................................................................................. 63

6.2.2 Design theory of C-type high-pass filter ................................................................. 65

6.2.3 Parameter design of C-type high-pass filter ........................................................... 67

6.2.4 Results analysis ....................................................................................................... 68

6.3 Active power filter ............................................................................................................. 70

6.3.1 Fundamental of active power filter ........................................................................ 70

6.3.2 Design of LCL active filter ....................................................................................... 71

6.3.3 Results analysis ....................................................................................................... 73

6.4 Summary ........................................................................................................................... 75

Chapter 7 Conclusion ...................................................................................................................... 77

7.1 Conclusion ......................................................................................................................... 77

7.2 Future Work ...................................................................................................................... 78

Appendix ......................................................................................................................................... 79

A. Offshore Wind Farm Test Case ........................................................................................ 79

B. Mathematical model of APF in ip-iq detection algorithm ............................................... 82

C. Control modes adopted in the converter station ............................................................ 83

D. Subsea cable parameters from ABB .................................................................................... 88

Reference ........................................................................................................................................ 90

List of figures

Fig. 2-1: Parallel resonance circuit and phase diagram ................................................................... 18

Fig. 2-2: Impedance in a parallel resonance circuit ......................................................................... 18

Fig. 2-3 Series resonance circuit and phase diagram ...................................................................... 19

Fig. 3-1: Wind turbine power characteristics .................................................................................. 22

Fig. 3-2: 𝐶𝑝- 𝛽 characteristics for different values of the pitch angle 𝛽 ....................................... 23

Fig. 3-3: Power Curve vs Wind Velocity ........................................................................................... 24

Fig. 3-4: Fixed Speed Wind Turbine Generator ............................................................................... 25

Fig. 3-5: Limited Speed Wind Turbine Generator ............................................................................ 25

Fig. 3-6: Variable Speed Wind Turbine with Partial Scale Power Converter.................................... 26

Fig. 3-7: Variable Speed Wind Turbine with Full Scale Power Converter ........................................ 27

Fig. 3-8: Radial clusters configuration ............................................................................................. 28

Fig. 3-9: Ring (left) and star (right) clusters configurations [61] ........................................................ 28

Fig. 3-10: An MVAC-collection grid for an offshore wind farm [43] ................................................ 29

Fig. 3-11: An MVDC-collection grid for an offshore wind farm ....................................................... 29

Fig. 3-12: Structure diagram of an offshore wind power plant ....................................................... 30

Fig. 3-13: Configuration of LCC-HVDC transmission system to shore ............................................. 31

Fig. 3-14: Configuration of VSC-HVDC transmission system to shore ............................................. 32

Fig. 3-15: Transmission solutions with power range vs distance [14] ............................................. 33

Fig. 4-1: Configuration of PMSG based wind energy generation system ........................................ 34

Fig. 4-2: Inner construction illustration of wind turbine ................................................................. 35

Fig. 4-3: wave form of machine-side and grid-side converter current ............................................ 36

Fig. 4-4: harmonic characteristics of machine-side converter current (x-axis: harmonic frequency

[Hz]) ................................................................................................................................................. 37

Fig. 4-5: harmonic characteristics of grid-side and grid-side converter current (x-axis: harmonic

order) .............................................................................................................................................. 37

Fig. 4-6: Wave form of grid-side converter current before and after filter ..................................... 38

Fig. 4-7: Harmonic characteristics of current before and after filter .............................................. 39

Fig. 4-8: The electrical system for the HVAC (a) and VSC-HVDC (b) transmission system of offshore

wind farm ........................................................................................................................................ 40

Fig. 4-9: The schematic diagram of the simulation system of VSC-HVDC ....................................... 42

Fig. 4-10: The schematic diagram of the simulation model of converter station in flexible DC

system ............................................................................................................................................. 43

Fig. 4-11: FFT bar plot of offshore wind power grid system at PCC point ....................................... 43

Fig. 4-12: THD bar plot of current harmonics at the connection point to the onshore .................. 44

Fig. 5-1: Direct-driven variable speed wind turbine based on permanent magnet synchronous

generator ......................................................................................................................................... 47

Fig. 5-2: High frequency harmonic model of grid-side converter including L filter......................... 48

Fig. 5-3: High frequency harmonic model of grid-side converter including LCL filter ..................... 48

Fig. 5-4: Low frequency harmonic model of grid-side converter .................................................... 49

Fig. 5-5: Equivalent circuit for harmonic model of transformer ...................................................... 50

Fig. 5-6: Equivalent circuit for harmonic model of submarine cable .............................................. 51

The parameters of the equivalent circuit can be calculated by the following formulas: ................ 51

Fig. 5-8: The structure of three-phase VSC ..................................................................................... 52

Fig. 5-9: Equivalent circuit for harmonic model of PMSG grid-side converter ................................ 54

Fig. 5-10: Equivalent circuit for harmonic model of transformer .................................................... 54

Fig. 5-11: Equivalent circuit for harmonic model of submarine cable ............................................ 54

Fig. 5-12: Equivalent circuit for harmonic model of VSC-HVDC grid-side converter ....................... 55

Fig. 5-13: Equivalent circuit for harmonic model of HVAC transmission system and the onshore

grid .................................................................................................................................................. 55

Fig. 5-14: Harmonic Impedance of Offshore Wind Farms with HVAC transmission system ........... 57

Fig. 5-15: Comparison between HVAC and HVDC Harmonic Model of Offshore Wind Farms ........ 58

Fig. 5-16: Frequency characteristics of cable impedance with different lengths ............................ 59

Fig. 5-17 (a) Frequency characteristics of cable impedance with different inductances ................ 60

Fig. 5-17 (b) Frequency characteristics of cable impedance with different inductances (detail) ... 60

Fig. 5-18(a) Frequency characteristics of cable impedance with different capacitances ................ 61

Fig. 5-18(b) Frequency characteristics of cable impedance with different capacitance values

(detail) ............................................................................................................................................. 61

Fig. 6-1: Five common passive filters [57] ....................................................................................... 64

Fig. 6-2: The circuit diagram for C-type high pass filter .................................................................. 65

Fig. 6-3: Spectral diagram of current harmonics at PCC without filters .......................................... 67

Fig. 6-4: The model of wind farm with the C-type filter .................................................................. 69

Fig. 6-5: The simulation model of C-type high pass filter ................................................................ 69

Fig. 6-6: The harmonic spectrum analysis diagram without and with the C-type filter .................. 69

Fig. 6-7: The harmonic spectrum analysis diagram before and after the access of C-type filter .... 70

Fig. 6-9: The schematic diagram of active filter .............................................................................. 71

Fig. 6-10: Overview diagram of the LCL active filter [66] ................................................................ 72

Fig. 6-11: Model diagram of APF’s access ....................................................................................... 73

Fig. 6-12: Configuration of the LCL filter ......................................................................................... 74

Fig. 6-13: The harmonic spectrum diagram without and with the LCL active filter ........................ 74

Fig. 6-14: The THD bar plot of the system without and with the LCL active filter .......................... 75

Fig. A-1: The electrical system for the HVAC (a) and HVDC (b) connection of the 160 MW offshore

wind farm ........................................................................................................................................ 79

Fig. A-2: harmonic model of HVAC transmission system in OWF .................................................... 80

Fig. A-3: harmonic model of HVAC transmission system in OWF .................................................... 81

Fig. B-1: Vector diagram between ip, iq in α-β coordinate system ................................................. 82

Fig. C-1: The AC voltage amplitude controller (AVAC) ..................................................................... 85

Fig. C-2: The active power controller .............................................................................................. 85

Fig. C-3: The d-axis orientation position ......................................................................................... 86

List of tables

Table 2-1: THD Limits (% of the fundamental) ................................................................................ 15

Table 4-1: Parameters for 2MW wind turbine ................................................................................ 35

Table 4-2: Harmonic characteristics of current from machine-side and grid-side converter .......... 37

Table 4-3: Harmonic characteristics of grid-side converter before and after the filter .................. 39

Table 4-4: Parameters of Low Capacity mid-voltage set cable ........................................................ 41

Table 4-5: Parameters of Submarine cable (33kV high capacity mid-voltage set cable) ................. 41

Table 4-6: Parameters of Booster Substation .................................................................................. 41

Table 4-7: Parameters of AC 230kV Undersea Cable System .......................................................... 41

Table 4-8: Parameters of Converter Station .................................................................................... 42

Table 5-1: Offshore wind turbine harmonic model parameters ..................................................... 56

Table 6-1: Simulated system specification ...................................................................................... 67

Table D-1: Parameters for 30kV three-core cables with copper wire screen .................................. 88

Table D-2: 10-90kV XLPE 3-core cables ........................................................................................... 89

Chapter 1 Introduction

1.1 Background and Motivation

As we all know, wind power is a kind of intermittent and random energy affected

by varied wind speed, season, region and climate. With the increasing scale of

offshore wind farms, a series of power quality problems will be produced for the

onshore grid [1]. The power fluctuation has great influence on the power flow,

especially when the wind power output fluctuation is strong, it is easy to cause the

voltage fluctuation. At the same time, the interaction between the transient change of

power and the voltage feedback control devices in the system will probably lead to

voltage flicker problems [2]. In addition, the power electronic equipment is another

potential source of harmonics. The generated harmonics will cause great threat to the

safety and stability of the system [3].

At present, the non-linear power electronic devices in the process of wind energy

conversion play a very important role [4]-[6]. The most common types of wind

turbine applied in the large scale offshore wind farm system are the variable speed

wind turbine generator with partial scale power converter or with full scale power

converter. For the offshore wind farm, a large number of submarine cables with high

distributed capacitance are used in the transmission system, which will cause the

system harmonic problems more serious [7]. In addition, when the cables are

connected with the transformers or other inductive components, the parallel resonance

is easy to occur in the system, which will increase the harmonic current distortion rate

and distortion level.

In large scale offshore wind farm, full-rated converters are applied in the offshore

wind farm construction, which makes the harmonics generated from those power

electronic devices more complex compared with the conventional harmonic

components. The difference of harmonic response is mainly reflected in the different

frequency range of the output harmonics. In addition, the complexity of the response

characteristic of the power electronic devices around low-frequency band is also very

high, and the harmonic impedance also has a great influence on the resonance point of

the offshore grid system. The resonance phenomena has amplification impact on the

harmonic characteristics of the system. This will cause the harmonic level injected

into the onshore grid several times higher than that of the individual turbines [8]. A

large area of cable laying also cause the resonance point more complex to be

estimated.

The trend for development of offshore wind farms is towards a growing size of

installed power. This together with higher distances from the shore leads in many

cases to HVAC and HVDC connection as a preferred choice for power export [9]. The

complex non-linear electronic devices for the control system of these transmission

systems are also challenging the existing system. At the same time, the grid topology

applied in offshore wind farm determines the length, electrical parameters and

connection methods of the cable, and directly affects the harmonic generation,

resonance frequency and its intensity. The lack of consideration of collection grid will

lead to less accurate harmonic analysis. The harmonic subject is however rarely taken

up in discussion about the effect of the collection grid of the offshore wind farm,

which could be an interesting study direction.

In electrical power system, a harmonic is defined as the content of the signal with

an integral multiple of the fundamental frequency. Non-linear components, including

transformers, converters, electrical machines, non-linear load, produce harmonics in

the system. Since the system is interconnected together, the harmonics can create

unpredicted stresses to the system and they can propagate over great distances within

the whole network, especially in an offshore wind farm. The harmonics in the system

could attenuate the stability of the system control and reduce the voltage quality. The

harmonic levels in the network could be amplified by resonance phenomenon [3].

Moreover, harmonics could also cause the overheating of the electrical components in

the network which may damage their insulation. These bad effects show that

harmonics reduce the efficiency of both the wind energy conversion system (WECS),

and the power utilization.

Since the uncertainty of wind resources and the characteristics of the wind turbine

generator, the output power of WECS exhibits fluctuation and intermittent nature,

which easily results in harmonic problems. Furthermore, offshore wind farms are

installed in remote sea, far from conventional generations. Therefore, in order to have

high quality power supplies from offshore wind farms, evaluating the harmonic

emission levels at the point of common coupling (PCC) has already been an urgent

demand. However, directly measuring and monitoring harmonics, particularly on high

voltage transmission network, can be very challenging [10]. Thus, the system

modeling and harmonic analysis in computer simulation programs can be a proper

way to estimate the potential harmonics and help to find solutions to improve the

power quality based on the study results.

1.2 Problem Description

The trend for offshore development of wind farms is towards a growing size of

installed power. This together with higher distances from the shore leads in many

cases to HVDC connection as a preferred choice for power export. In this thesis work,

an offshore wind farm model consisting of full-scale converter wind turbines, is

proposed in MATLAB/Simulink. It is important that the models built for analyzing

the harmonics are practical and appropriate. However, offshore wind farms involve

multiple suppliers of wind turbines, cables, transformers and other devices. The

design details of each components in the system required by system modeling and

analysis are kind of impossible to get. Majority of related research work assume the

wind farm as an ideal voltage source or an equivalent constant power grid, which

ignore the fluctuation and intermittent nature of wind farms and the collection grid

network. This thesis work is considered to build a numerical model for a large scale

offshore wind farm and to investigate the potential influence factors in the wind farm,

such as the individual wind turbine, the collection grid network, the transmission

system type. Hopefully after the thesis work, an overall scope and understanding of

the harmonic problems and resonance phenomenon in the large scale wind farm could

be established. And finally some effective methods should be recommended to reduce

the harmonic problems.

1.3 Objective and Scope

The objective of this master thesis is to discuss the harmonic problems which may

occur in the collection grid of the large scale offshore wind farm (OWF) and try to

validate a practical simulation modelling and harmonic analysis approach for OWF.

This topic can furthermore be divided into several sub-topics:

Wind farm collection grid and transmission system modeling

Harmonic resonance analysis by frequency scan method

Time-domain circuit simulation and harmonic FFT analysis

The scope of the thesis work is set as follows:

Target System- a simple offshore wind farm collection grid in radial topology is

modeled and studied in MATLAB/SIMULINK. The wind farm employs a 2MW

permanent-magnet synchronous generator and a back-to-back full power

conversion system (Type 4 turbine). The offshore transmission system is

equipped with 100kV HVDC export submarine cables and substation converters.

The onshore transmission system and the ac power grid is assumed to be a stable

and ideal infinite power supply.

Testing Method- all the analysis are performed in MATLAB/SIMULINK and the

conclusions drawn from the simulation results. No practical experiments are

involved.

Harmonic field- the investigation scope of harmonics limits to maximum of 30th

order. And the study will only focus on odd order harmonics. No considering of

inter-harmonics.

Analysis Method- FFT analysis tool for measuring THD at the connection point

between the target offshore wind farm collection grid and the onshore power grid.

Frequency scan method for harmonic resonance analysis on the equivalent

harmonic model of the target offshore wind farm collection grid.

Exclusions- the following aspects are not considered in the project:

The effect of control strategy to the harmonic emission

The detailed modeling of the collection grid assumes ideal switches and well

protected

1.4 Report Layout

This thesis report is organized as follows:

Chapter 1 introduces an overview of the work objective and background.

Chapter 2 gives an overview about the essential definitions and basics referred to

harmonics. The subsequent part shows the theory of harmonic resonance and potential

causes in offshore wind farm. The frequency scan method and time domain harmonic

analysis based on FFT calculation in numerical simulation model are introduced, for

further analysis foundation.

Chapter 3 interprets the basic of wind turbine and offshore wind farm installation. It

describes the composition and structure of collection grid for offshore wind farms,

including the common collection grid topology, MVAC or MVDC collection grid,

transmission system category, and compares the advantages and disadvantages

introduced followed.

Chapter 4 establishes the type 4 PMSG wind turbine based on the model example

from MATLAB. Harmonic current output characteristics of the machine-side

converter and the grid-side converter are analyzed by the FFT analysis tool in

Simulink. The model for an investigated offshore wind farm is validated in simulation.

Harmonic output characteristics of the offshore wind farm is also analyzed.

Chapter 5 builds the harmonic model of offshore wind farm installation, simulates

the system in equivalent impedance circuit. And then the frequency scan method is

applied to detect the influence components which potentially affect the harmonic

resonance. Give an approximate forecast of the theoretical resonance point.

Chapter 6 studies on the strategy for suppressing harmonics at the offshore wind

farm. By introducing the characteristics and working principle of filters, a C-type

filter and an active power filter adopted in the system are designed and analyzed with

simulation models. We have also mentioned three effective methods to optimize the

system network structure to help suppressing harmonics.

Chapter 7 draws the main conclusions from this project and gives some suggestions

for future research work.

Chapter 2 Basic of Harmonics The fundamental theory about harmonics are introduced in this chapter, including

the definition and several indices referred to harmonics, such as Total Harmonic

Distortion. The potential harmonic sources in the offshore wind farm are discussed

and investigated as follows. The subsequent part shows the theory of harmonic

resonance and potential causes in offshore wind farm. The last part explains the

research method related to the analysis of the harmonics and resonance.

2.1 The Definition of Harmonic

Harmonics are steady-state distortions to current and voltage waves and repeat

every cycle in power system. The harmonic can be simply expressed as

𝑓ℎ = ℎ ∙ 𝑓 (2-1)

Terms that have represent the harmonic components of the current (or voltage).

Several points need to be emphasized:

1) The harmonic order h is a positive integer (ℎ = 1, 2, 3, …𝑛). And the term 𝑓ℎ is

the frequency of the h order harmonic. When ℎ = 1, it represents the fundamental

frequency, which is usually 50Hz in Europe countries or 60 Hz in America

countries.

2) When ℎ < 1, which means the sinusoidal waves are the below the fundamental

frequency, those kind of components are called the sub-harmonics. When any

non-integer values of ℎ occur, it means that the voltages or the currents have

frequency between the harmonics, those kind of components are called inter

harmonics [11]. Both sub-harmonics and inter harmonics will not be included in

the research scope of this thesis paper.

3) According to the basic concept of Fourier series, the waveform of transformation

must be periodic and relatively unchangeable. Although in the actual operation

situation, due to the complex changes in power system conditions, it is impossible

to achieve infinite waveform unchanged, thus it will take some time to apply the

Fourier transform. Therefore, harmonic phenomena and transient phenomena need

to be distinguished.

4) It is necessary to distinguish between short time harmonics (such as impulse

currents, etc.) and steady-state or quasi-steady-state harmonics.

2.2 Total Harmonic Distortion (THD)

The total harmonic distortion (THD) is an important parameter that could represent

the harmonic distortion level of voltage or current signals. It is defined as the ratio of

the sum of the powers of all harmonic components to the fundamental frequency

component. Taking voltage as an example, THD is an index to compare the harmonic

voltage components with the fundamental voltage component, as the following

equation defines it mathematically.

THD =√∑ 𝑉ℎ

2𝑛ℎ=2

𝑉1=

√𝑉22+𝑉3

2+⋯+𝑉𝑛2

𝑉1 (2-2)

Where the variable h is the number of harmonic, and n is the maximum harmonic

order of voltage, 𝑉1 is the nominal system voltage at the fundamental frequency [12].

Generally, the analysis of harmonics is considered below the 51th order, since the

higher range of frequency components have little power to influence the stability of

the power grid. Total harmonic distortion can be expressed also in per cents.

Theoretically, the smaller the value of THD measured in any output signal of one

system, the degree of distortion is lower at that signal.

On the analogy of this, the similar parameter for measuring the current distortion is

called the total harmonic current distortion (THDI), as following equation [13]

THDI =√∑ 𝐼ℎ

2𝑛ℎ=2

𝐼1=

√𝐼22+𝐼3

2+⋯+𝐼𝑛2

𝐼1 (2-3)

For the evaluation of power quality related to levels of harmonic distortion, there is

recommended limits standard for THD (and THDI) in an electrical distribution system

at the point of common coupling (PCC) that must be obeyed in industry facility. The

PCC is the point between the non-linear load and its connection to a power source,

either the serving utility or an on-site generator. [6].

The ANSI/IEEE 519-1992 standard lists is recommended to be one of the most

widely used guide for THD limits in a power grid system [36]. Thus, one objective of

harmonic analysis is to assist the system design and installation in meeting IEEE

519-1992 requirements limiting THD, as shown in Table 2-1.

Table 2-1: THD Limits (% of the fundamental)

PCC Voltage THD (%)

V ≤ 69 kV 5

69 kV < 𝑉 < 161 𝑘𝑉 2.5

V > 161 𝑘𝑉 1.5

2.3 Fast Fourier Transform (FFT)

As previously described, the total harmonic distortion (THD) interprets the

distortion degree between the waveform and the pure sine wave, characterized mainly

by the amplitude of voltage harmonics in the system, which is defined as the

percentage of the total harmonic content of the RMS value and fundamental RMS

ratio.

The analysis and calculation of harmonic distortion level is based on the algorithm

called Fast Fourier Transformation (FFT), proposed by American scientists in 1965.

In general, any periodic waveform could be expanded into Fourier series. For instance,

a periodic current signal could be expressed as following equation

i(t) = ∑ 𝐼ℎ cos(ℎ𝜔0𝑡 + 𝜃ℎ)𝑀ℎ=1 (2-4)

In which, 𝐼ℎ is the h order harmonic peak current, 𝜃ℎ is the phase of the h order

harmonic current [14], 𝜔0 is the fundamental angular frequency, M is the considered

highest order of harmonics, normally less than 50.

Fast Fourier Transformation is simply an algorithm that can compute the discrete

Fourier transform (DFT) much more rapidly and efficiently than other available

algorithms [14]. It does not require a detail understanding in the algorithm itself, but

rather be treated as a particular method and computation tool to obtain the amplitude,

frequency and phase etc. information of the harmonic signal [14], which has the

advantages of high precision, strong practicability. Thus, the FFT algorithm will not

be interpreted in detail in this thesis.

In the harmonic analysis of offshore collection grid, FFT can describe curves that

show the relationship between the orders of harmonics and interprets the THD values

at each order harmonic of the system. Thus FFT method laid a theoretical foundation

for exploring the factors affecting harmonics. And it is one of the most important and

widely used methods to research harmonics in the current stage.

2.4 Sources of Harmonics in Offshore Wind Farms

Harmonic problem is one of the main concern in the offshore wind farm installation,

where large number of subsea cables and converters are equipped. Wind farms are

known as sources of harmonic distortion. When analyzing the harmonics from a wind

farm system, two main emission sources of harmonics should be considered.

Harmonic Emission from Individual Wind Turbine

The first common concern is the harmonic emissions from individual wind turbines

[8]. Theoretically, the harmonics generated from wind turbine generators will flow

into the entire collection grid of the offshore wind farm, and will cause the harmonic

distortion level more severe into the onshore grid. Generally, the harmonic emission

from individual wind turbines mainly comes from power-electronic converters,

induction machines and power transformers. Nowadays large size wind turbines in

MW capacity usually contain converters, normally could be a full scale power

converter or a partial-size converter. However, quite a lot research have already

focused on this topic. And it turns out that the level of harmonic output from wind

turbines is relatively small [8]. The harmonics are influenced by the converter control

strategy and switching frequency of electronic devices. Only some relatively high

emission occurs at higher harmonic orders, which is lack of enough power to

influence the voltage quality of the whole grid system, and for other frequencies

where the distortion levels are traditionally lower.

Harmonic Emission from the Wind Farm Collection Grid

The impact of the wind farm collection grid on the harmonic emission has not been

studied in very detail, but harmonic resonances have been widely studied [27]-[29].

The collection grid in one offshore wind farm can consist capacitance of large amount

of subsea cables and the inductance of the transformers, which will induce the

resonance problem occur. In this case, the harmonic emission from the wind farm into

the onshore grid is several times higher than that of the individual turbines. In this

thesis work, the one consideration target is on the potential influence of the collection

grid to the harmonic propagation and related resonance issues.

2.5 Harmonic Resonance

2.5.1 Introduction

In an electrical system, the capacitance appears in the form of cables, overhead

lines, or capacitor banks, while the inductance appears in the form of cable lines,

transformers. A reactance of an electrical network is dependent on the frequency. At

certain frequencies the inductive and capacitive components of the network start to

resonate with each other at the resonance frequency. When the harmonic current is the

same as the resonant frequency, the harmonic current or voltage will be amplified. In

that way, the harmonic problem will become more severe [30]. The resonance

frequency can be calculated as

f =1

2𝜋√1

𝐿𝐶 , (2-4)

Where L is the inductance and C is the capacitance of the network.

Two different types of harmonic resonances can be distinguished: parallel

resonances and series resonances [8], discussed in Sections 2.5.2 and 2.5.3. The

components that make the power system more likely to experience resonances are

discussed in Section 2.5.

2.5.2 Parallel Resonance

At parallel resonance, the parallel LC tank circuit acts like an open circuit with the

circuit current being determined by the resistor, R only. At resonance, the impedance

of a parallel resonance circuit at resonance is at its maximum value and equal to the

value of the resistance R in the circuit. Also at resonance, as the impedance of the

circuit is now that of resistance only, the total circuit current, I will be “in-phase” with

the supply voltage.

When the parallel resonance occurs, the harmonic current is excited to oscillate

between the inductive energy storage and the capacitor energy storage. Then parallel

circuits produce current resonance. Then overvoltage become easier to occur. At the

same time, it could result in an amplification of the harmonic current, thus the current

elsewhere in the gird could be higher than that close to the source of the distortion [8],

as illustrated in Fig. 2-1.

Fig. 2-1: Parallel resonance circuit and phase diagram

Fig. 2-2: Impedance in a parallel resonance circuit

It has a negative impact on every wind farm component, and eventually it will

damage the system. The parallel resonance is common when there are capacitor banks

or long AC lines connected with large transformers. Hence, for the offshore wind

farm collection grid with large amount of those nonlinear components, the parallel

resonance is a hidden danger that can result in the harmonic distortion level at PCC

several times higher than that of individual turbines [8]. In an extreme case, even a

relatively small harmonic current can cause destructively high voltage peaks at

resonance frequency.

2.5.3 Series Resonance

During series resonance, the inductive reactance of system components (such as

transformers) is equal to the capacitive reactance of system components (such as

cables or capacitor banks) as shown in following equations. This would cause the

impedance of the circuit very low.

ωL =1

𝜔𝐶 (2-5)

The natural resonant frequency will be:

f =1

2𝜋√𝐿𝐶 (2-6)

When 𝑋𝐿 = 𝑋𝐶 ≫ 𝑅 , then 𝑈𝐿 = 𝐼0𝑋𝐿 = 𝑈𝐶 = 𝐼0𝑋𝐶 ≫ 𝑈 = 𝐼0𝑅 , where 𝑈

represent the system equivalent voltage source. Though these inductive and capacitive

high voltages drop 𝑈𝐿, 𝑈𝐶 will have opposite signs, which makes the sum of the two

voltages be zero, but each of them will still have high amplitude, as presented in the

phase diagram below. The point at which this occurs is called the resonant frequency

point of the circuit.

Fig. 2-3 Series resonance circuit and phase diagram

2.6 Harmonic Analysis Methods

2.6.1 Introduction

Harmonics analysis in this thesis report has two main stages. The first step is the

frequency scan method to identify resonance frequencies [15]. The second one is to

perform time-domain simulation to calculate harmonic distortion indices, mainly refer

to THD values at the collection point.

2.6.2 Frequency Scan Method

The usual method for analyzing harmonic impedance characteristic is the

impedance scan method, which is also called frequency scan method. It is an

approximate linearization analysis method. The core of impedance scan method is to

describe the whole system impedance versus frequency curve from the studied

component sight, which includes two kinds curve plot, reactance versus frequency

curve and resistance versus frequency curve. Its principal objective is to detect the

possible resonance frequencies at which parallel and/or series resonance can occur in

the electrical network.

The impedance seen at a bus is calculated at all frequencies, sweeping or scanning

the frequency spectrum of interest. It can be treated as being performed by injecting a

1A sinusoidal current with a certain frequency at this bus and calculating the

corresponding voltage which consequently corresponds to the impedance at this bus.

This process is repeated for all frequencies within the range of interest [15]. The

result of this calculation is a plot of the magnitude of the driving point impedance at a

certain bus (on the vertical axis) versus the harmonic frequency (or the harmonic

order) (on the horizontal axis). Then the relation between the magnitude of impedance

and the frequency (or harmonic order) is obtained, and the potential resonance point

of the system could be observed. A high value (a sharp peak) of impedance at certain

frequency means the network is having parallel resonance at this frequency. When

parallel resonance happens, relatively small excitation current can generate large

voltage amplification. A near zero value (a sharp dip) of impedance at certain

frequency means the network is having series resonance at this frequency [15]. When

series resonance happens, relatively small excitation voltage can cause large current

amplification.

In this thesis, the frequency sweep impedance plot presents the magnitude and

angle of the network impedance calculated at PCC (Power Collection Point). In

another word, this method measures impedance of circuit as function of frequency.

In Chapter 4, frequency scan method is used to monitor these possible dangerous

resonance phenomenon, and also to analyze the potential influence of those electric

devices in the OWF system.

2.6.3 Time-Domain Harmonics Analysis

Time-domain analysis is also called transient simulation. The time domain

formulation consists of differential equations representing the dynamic behavior of

the interconnected power system components. The resulting system of equations,

generally non-linear, is normally solved using numerical integration [16]. It is

normally used to verify results of other frequency analysis algorithms.

Time-domain analysis requires considerable computation even for relatively small

systems. Another problem attached to time domain algorithms for harmonic studies is

the difficulty of modelling components with distributed or frequency-dependent

parameters [17].

In the time domain analysis, simulation is performed for sufficient time to reach

steady state conditions using digital simulators, such as PSCAD, MATLAB,

PowerFactory. The resulting waveforms are then analyzed using FFT to determine

harmonic components of currents and voltages under investigation. Consequently

harmonic distortion indices are calculated. In this thesis, MATLAB/Simulink software

is applied in time domain harmonic analysis. Simulink provides an integrated

environment for modeling, simulation, and integration of dynamic systems. In this

environment, a complex system can be constructed without a large number of writing

programs, and only by simple mouse operations.

2.7 Summary

All in all, this chapter gives an overview about the basics of harmonics, including

some essential definitions and indices, such as Total Harmonic Distortion (THD). The

subsequent part shows the theory of harmonic resonance and then discuss the

potential causes in the offshore wind farm (OWF). The last part explains the research

method for harmonics and resonance analysis. The frequency scan method and time

domain harmonic analysis based on FFT calculation in numerical simulation model

are introduced, for further analysis foundation.

Chapter 3 Basics of Offshore Wind Farm

System In general, an offshore wind farm (OWF) mainly consists of wind turbine generator

(WTG), collection grid, transmission system. Thus, the harmonic characteristics from

OWF will be complicated cases of different categories of wind turbine generators, the

electric configuration of converters, the collection grid topology and the transmission

system in either HVAC or HVDC. This chapter, the basic theory about offshore wind

farm system is described as the fundamental for the model building and harmonic

analysis of the offshore wind farm system.

3. 1 Wind Turbine Fundamentals

3.1.1 Wind Turbine Characteristics

The model is based on the steady-state power characteristics of the turbine. The

output power equation of the wind turbine is given by the following equation:

P =1

2𝜌𝑉0

3𝐴𝐶𝑝(𝛽, 𝜆) (3-1)

Where 𝑉0 represents the wind speed (m/s), 𝜌 is the air density (kg/m3), 𝐴 is the

turbine swept area (m2), 𝐶𝑝 is the performance coefficient of the turbine. 𝐶𝑝 is a

function of pitch angle 𝛽 (degree) and tip speed ratio of the rotor blade tip speed to

wind speed 𝜆 =𝜔𝑅

𝑉0, where 𝜔 is the angular rotor speed for the wind turbine.

Fig. 3-1: Wind turbine power characteristics

The analytical approximation method used to calculate 𝐶𝑝 is given by the

following equations:

𝐶𝑝(𝛽, 𝜆) = 0.5176 (116

𝜆𝑖− 0.4𝛽 − 5) 𝑒

−21

𝜆𝑖 + 0.0068𝜆 (3-2)

1

𝜆𝑖=

1

𝜆+0.08𝛽−

0.035

𝛽3+1 (3-3)

Fig. 3-2: 𝐶𝑝- 𝛽 characteristics for different values of the pitch angle 𝛽

3.1.2 Operation Modes of Wind Turbine

The tasks of the turbine’s control system include the start and stop of the turbine,

power output limitation, optimization of power output and efficiency, keeping the

rotational speed within a certain range, minimization of power fluctuations and

mechanical loads. The following figure shows the ideal operation status under the

changing of wind speed, which can be categorized to three operation modes.

Fig. 3-3: Power Curve vs Wind Velocity

Zone 1: 𝑉𝑤𝑖𝑛𝑑 < 𝑉𝑐𝑢𝑡−𝑖𝑛 or 𝑉𝑤𝑖𝑛𝑑 > 𝑉𝑐𝑢𝑡−𝑜𝑢𝑡

The power output of turbine should be zero. In this operation mode, the task of the

control system is the start and stop of the turbine.

Zone 2: 𝑉𝑐𝑢𝑡−𝑖𝑛 ≤ 𝑉𝑤𝑖𝑛𝑑 ≤ 𝑉𝑟𝑎𝑡𝑒𝑑

The blade pitch angle is set fixed to its optimal value that allows the turbine to extract

maximum energy from incident wind [18]. The wind turbine rotational speed ω is

controlled to keep the tip speed ratio λ at its optimal value. In this operation zone, the

wind turbine is controlled by MPPT control scheme to optimize the power output.

Speed control loop bandwidth must be limited within around 2 rad/s in order to obtain

a smooth power output [19].

Zone 3: 𝑉𝑟𝑎𝑡𝑒𝑑 < 𝑉𝑤𝑖𝑛𝑑 ≤ 𝑉𝑐𝑢𝑡−𝑜𝑢𝑡

When the wind speed is greater than the rated wind speed, in order to limit the power

output, the wind turbine is controlled by the pitch regulation. To avoid over rated

power excursions due to wind gusts, a constant power reference is obtained by

reducing torque (with the increase of rotational speed). In another words, if the wind

speed is larger than the rated speed, then the output power command of the PMSG

𝑃𝑔∗ is set to 1pu [20].

3.1.3 Category of Wind Turbine Generators

As the fast development of offshore wind farm technology, the harmonic problems

turn out to be more complicated and severe. The harmonic and resonance problems of

offshore wind farms vary from each other according to the various types of wind

turbine generators, electric configuration and control strategy of converters, the

Standstill

Region Normal

Operation

Region Pitched Operation Region

capacitance to earth from undersea transmission cables, etc. The technology of wind

turbine generators change from previous fixed-speed induction generator with small

rating power to various speed wind turbine generator with much larger rating power.

The generators for wind turbines are categorized into following four major types,

fixed-speed induction generator (FSIG), doubly fed induction generator (DFIG), and

full power converter (FPC) synchronous or asynchronous generators [21]. The

overview of wind turbine concepts are described as following.

Fixed Speed Wind Turbine Generator

Fixed speed wind turbines comprise of squirrel cage asynchronous generator

(SCIG). Its rotor is driven by the turbine and its stator is directly connected to the grid.

This type wind turbine generator has the limitation that any wind fluctuation will

result into the fluctuations of the mechanical torque and the electrical power, which

lead to voltage fluctuation and flicker effects in the case of weak grid.

Fig. 3-4: Fixed Speed Wind Turbine Generator

Limited Speed Wind Turbine Generator

Limited variable speed wind turbines are usually equipped with a wound rotor

induction generator (WRIG). The rotor electrical resistance is changed through power

electronics to allow both the rotor and the generator to vary their speed up and down

to ±10% of synchronous speed. It’s also called variable slip operation. And this type

design concept helps reduce the mechanical stress of the turbine and maximize the

power quality. Aerodynamic control method of limited speed wind turbine is active

blade pitch control.

Fig. 3-5: Limited Speed Wind Turbine Generator

Variable Speed Wind Turbine Generator with Partial Scale Power Converter

This type turbine generator is also known as doubly-fed induction generator

(DFIG). The stator of the generator is connected directly to the grid and the windings

of the rotor are connected to a partial scale power converter [22], as shown in Fig.

3-6.

Fig. 3-6: Variable Speed Wind Turbine with Partial Scale Power Converter

The harmonics in DFIG mainly come from three aspects: the first is the natural slot

harmonic and saturated air gap in the structure of asynchronous generator. Secondly,

the AC excitation flowing to the grid network provided by the various speed

generation system with large rating power will potentially threaten the grid. Thirdly,

harmonics from the grid network could also be a source.

DFIG type wind turbine is commonly used because of its small capacity excitation

converter, low cost and high efficiency. But the use of DFIG will lead to serious

harmonic problem, many studies have been done about it in recent years.

Variable Speed Wind Turbine Generator with Full Scale Power Converter

While a partial scale power converter is needed for DFIG, the full scale power

converter is needed for this Type D generator configuration [13]. The wind turbines

are equipped with the classical drive-train (geared), in the direct drive concept

(without gear box, slow running generator). And various types of generators could be

used in this type wind turbines: permanent magnet synchronous generator (PMSG),

wound rotor synchronous generator (WRSG), and wound rotor induction generator

(WRIG) [23], shown as Fig. 3-8. Since being completely decoupled from the grid, it

can provide wider range of operating speed than type C, and has a broader range of

reactive power and voltage control capacities [24].

Fig. 3-7: Variable Speed Wind Turbine with Full Scale Power Converter

Compared to the DFIG, PMSG has lower operation and maintenance cost, simpler

structure, smaller noise and higher energy conversion efficiency, especially for large

rating power generators. Therefore, the market share of large capacity wind power

generator based on PMSG is increasing. At the same time, more and more wind power

manufacturers favor this type of wind turbines in industry market.

In the future, long distance and large scale offshore wind farms will be more

inclined to adopt PMSG power generation system. At present, there is not much

research on harmonic analysis of PMSG power generation system, compared to the

study of DFIG. Based on the above analysis, this paper takes offshore wind farm

equipped with PMSG wind turbines as the object of study, and studies the harmonic

and resonance problems of the collection grid in offshore wind farm installations.

3.2 Collection Grid in Offshore Wind Farm

3.2.1 Collection Grid Topology

In common cases, the capacity of a single wind turbine in offshore wind farms is

several MW, thus the total capacity of a medium or large scale offshore wind farm

connected to the onshore grid could be several hundred MW or several thousand MW.

They need the collection grid to interconnect all the wind turbine generators (WTG)

to fulfill the long distance transmission. In fact, the collection grid topology of the

offshore wind farm decides the length of undersea cables, electric parameter settings

and connecting configuration, which directly influence the harmonic emission of the

system, resonance frequency and intensity. Lacking the consideration of collection

grid topology will lead to inaccuracy of harmonic analysis. Thus, before stepping into

the harmonic analysis of the offshore wind farm connected to the grid, the collection

grid topology needs to be concerned.

In recent studies in the collection grid topology, researchers often focus more on the

economy and reliability, but much less on the harmonic analysis of the offshore wind

farm. The offshore collection grid have three alternative configurations so far: radial

(or string), ring and star cluster [41]. Considering the variety of wind farm capacity,

the distance to the onshore grid, the reliability of the system and other factors, the

collection grid topology of wind farm installation will have different choices. Since

the collection grid topology will result in different length of undersea cables, electric

parameter settings and connecting configuration of electronic devices, and those facts

have relatively large influence on harmonic resonance problems, thus affecting the

reliability of the offshore wind farm and its connecting onshore grid. The following

three alternative configurations of the collection grid topologies are introduced in

detail:

1) Radial

For radial clusters, the wind turbines inject their power into the same feeder in

string configuration. The feeder bus should have high enough voltage level to have

the capacity of the total power production of the string. In order to adapt WTG and

feeder bus voltages, each wind turbine need a set-up transformer.

This radial configuration has the advantages of simple operation and low cost, but

the disadvantage exists in the lack of reliability. Once the network cable or the

corresponding equipment needs to be repaired, the whole cable needs to be cut off. All

in all, the radial collection system is currently the most economical, common

collection grid topology. The radial collection grid topology has been more widely

adopted in many offshore wind farms, such as Horns Rev2 wind farm in Denmark.

Fig. 3-8: Radial clusters configuration

2) Ring

The ring topology is quite similar to the string topology, but the collection grid

connects each two independent string clusters to a closed ring cluster through cables.

For ring clusters configuration, it reduces the possibility of a cable failure and allows

auxiliary supplies to turbines be maintained. The system reliability is improved but

apparently costs more and the operation is relatively complex.

Fig. 3-9: Ring (left) and star (right) clusters configurations [61]

3) Star

For the star collection system, each single WTG is connected to a nodal point

directly through cables in small or medium capacity, where a transformer is installed

in the offshore platform. After the set-up transformer, the total generated power is

further brought to a central collection point through large capacity cables. The star

collection grid topology has high reliability, however, the disadvantage also exists.

The system needs more electric devices such as circuit breaker, isolating switch. Thus,

the cost is relatively higher than other topology. The wind farms generally do not use

this type of collection grid topology, unless in special demand.

Currently, the most cost effective collection voltage seems to be approximately

between 30kV to 36kV [42]. Only radial connection is the most common

configuration used in offshore wind farm projects thus far, therefore, this thesis work

also chose the radial cluster configuration for the wind farm installation.

3.2.2 MVAC/MVDC collection grid

When wind farms adopt HVDC transmission technology, MVAC or MVDC

collection grid can be used. When the power from MVAC collection system being

converted to HVDC transmission system, it needs large capacity transformer, power

electronic converter and other equipment as shown in Fig. 3-11. It is necessary to

build a large offshore platform; and the maintenance cost of the power frequency

transformer is high.

Fig. 3-10: An MVAC-collection grid for an offshore wind farm [43]

The wind farm using DC (MVDC)-collection grid has been considered as one of

effective solutions to solve these problems due to recent research. Several

configurations were evaluated with respect to overall system efficiency [43].

Fig. 3-11: An MVDC-collection grid for an offshore wind farm

Compared with MVAC collection grid, the layout of MVDC collection cables

avoids the problems of reactive charging current and potential resonance. And it also

requires that the output voltage of each turbine is at a certain level that there is no

need for a step-up transformer before the central converter of the farm. As a result,

switching losses are reduced [43]. Although the MVDC collection system also needs

the booster station, but power electronic converter for DC boost occupies a much

smaller space. Other benefits from this solution are less expensive generator drives

and more reliable systems, since one VSC less is utilized in each turbine [43].

3.3 Transmission System to Shore

3.3.1 Introduction

The majority of offshore wind power plants that are currently operating have

adopted an HVAC connection for the cabling to the shore (main ac grid). As the size

of future wind power plants and the distance to shore is likely to increase, more and

more planned offshore projects will be connected via HVDC (High voltage direct

current) transmission system [44].

Fig. 3-12: Structure diagram of an offshore wind power plant

For HVDC transmission system, there are two technical options: line commutated

converter (LCC)-based HVDC and voltage-source converter (VSC)-based HVDC

technology [45]. The HVDC system has been dominated by line commutated

converters (LCC); however, voltage source converters (VSCs) which include

two-level, multi-level and modular multilevel converters are increasing dramatically

due to having superior system performance and controllability [46].

3.3.2 HVAC Transmission

Currently, HVAC (High voltage alternating current) transmission system is the most

common solution adopted by the existing offshore wind farms. HVAC technology can

be economically used for the lower rated schemes over short distances [47]. And it

has following features:

1) The undersea AC cable generates large reactive current, which reduces the active

current carrying capacity of the cable. Limits of AC cable power ratings over

longer distances will probably not be improved enough to allow utilization of this

technology on larger wind farms [47].

2) Due to the long distance, the cable owns high capacitance, thus large reactive

power compensation device is often needed, which increases the cost and brings

troubles to the corresponding substation. Furthermore, high capacitance of the

cable may lead to resonances between the offshore and onshore grids. Then

voltage distortion may be a vital problem for the grid which need extra efforts to

fix with.

3) Compared to HVDC connections, the substations for HVAC is low cost, because

no power electronic devices (converters) are needed. But the cables are more

expensive than that for dc transmission system, when the transmission distance is

far away from the shore.

3.3.3 LCC-HVDC Transmission

LCC-HVDC (High voltage direct current with thyristor-based line-commutated

converters) transmission systems have proven its reliability on land in practical

industry for a while [48]. At present, it has gradually been used in the transmission

network. Due to its large capacity, long-distance transmission and simple control

strategy, LCC-HVDC technology has certain applicability for offshore wind power.

The whole grid connected transmission system is shown below.

Fig. 3-13: Configuration of LCC-HVDC transmission system to shore

The LCC-HVDC transmission system mainly includes transformer, SVC, filter,

thyristor converter, DC reactor, DC cable and other equipment. The normal operation

of the substation is based on the thyristor converter. Due to the characteristics of the

thyristor, a large number of reactive power need to be absorbed in order to operate

under normal condition, thus the collecting point need to be equipped with reactive

power compensation equipment, which will increase the cost and volume of the

offshore substation.

The conventional HVDC transmission system has following advantage features

compared to HVAC technology:

1) Frequency at the sending end can be variable. The ability to de-couple the

multiple turbines, and avoid synchronizing them with the onshore network has a

major advantage, as each end of the link may be allowed to operate according to

its own control strategy, largely independent of the other end.

2) Transmission distance is not a technical limitation. The impact of cable charging

current in AC cable interconnections is significant, even dominant, but in DC

applications it is negligible.

LCC-HVDC systems have proven its reliability on land in practical industry for a

while and could be cheaper than VSCs for power rating of hundreds of megawatts

[42]. But for offshore wind farms, the suitability should be considered carefully.

1) Converter and other electric equipment need space to install, which means

enormous offshore platform has to be built.

2) Furthermore, it is easy effected by ac network disturbances, which may lead to

converter commutation failures.

3) It requires reactive power and voltage support for offshore ac bus. Usually a static

synchronous compensator is essential to fulfill the network requirement [49].

3.3.4 VSC-HVDC Transmission

VSC-HVDC is a new type of power transmission and distribution technology with

power electronic technology as its core, which is gaining more and more attention. It

has only become possible as a result of important advances in the development of

insulated gate bipolar transistors (IGBTs). In this way, pulse-width modulation (PWM)

technology can be used for the VSCs as a means of control, as opposed to

thyristor-based LCCs used in the conventional HVDC technology.

Fig. 3-14: Configuration of VSC-HVDC transmission system to shore

HVDC-VSC technology has several advantages compared with LCC-HVDC.

1) VSC technology does not require commutation voltage supplied by compensator,

and the DC capacitor is enough for the reactive power provision.

2) Low order harmonics almost not existed thanks to the voltage and current control

uses PWM (pulse-width modulation) with switching frequency of several times of

the fundamental frequency [47]. And the harmonic distortion in ac side voltage is

lower in VSC-HVDC system, and fewer auxiliary filters are required compared

with LCCs.

3) The active and reactive power through undersea DC cable to the ac grid is

independently controlled. Thus, the voltage regulation is more effective due to the

robust control strategy. And the VSCs are able to operate in weak ac network, in

another word, the reliability of the system could be guaranteed.

3.3.5 Transmission System Selection

In general, offshore wind farm installed with rating power less than 150MW and

offshore distance within 100km can consider the HVAC transmission system.

Compared to the other two HVDC transmission system, the cost of HVAC collection

solution is much lower, which has economic superiority for industry installation.

When the installed capacity is between 100-400MW, the priority is given to the

HVDC transmission system. Considering the construction cost and installation

difficulty of the offshore converter substation, VSC-HVDC has more economic and

technological advantages than the traditional LCC-HVDC.

Fig. 3-15: Transmission solutions with power range vs distance [14]

For large scale offshore wind farms with power ratings above about 300 MW, it can

be seen that conventional LCC-HVDC technology is the optimum solution [50]. An

estimated comparison of the different transmission systems is as shown in Figure 3-16.

Therefore, considering the actual situation, we need to evaluate the specific choice of

transmission system connected to shore, within the consideration of installation

capacity, total cost, system reliability, and harmonic issues.

Chapter 4 Modelling and Harmonic Analysis

in Offshore Wind Farm

4.1 Wind Energy Generation System

4.1.1 Introduction

This following section presents the dynamic model of the individual direct drive

PMSG wind energy generation system [25]. The wind turbine generator considered in

this paper employs a direct-driven (without gearbox) PMSG directly coupled to the

wind turbine and connected to the electric grid through offshore collection grid [26].

The stator windings of the PMSG are connected to a full scale back-to-back ac/dc/ac

power converter which composed of a machine-side and grid-side converter with an

intermediate dc link [26]. The system configuration is shown in Figure 4-1.

Fig. 4-1: Configuration of PMSG based wind energy generation system

Wind turbine output power is sent to PMSG. To obtain maximum energy

production, the rotational speed of the PMSG is controlled by a PWM converter [27].

The machine side converter proposes the control schemes including a maximum

power point tracking (MPPT) control. The grid side converter is used to regulate the

dc voltage of the back-to-back converter, and the collection grid voltage. A simple LC

filter is also designed to filtering the possible ripple caused by the switching [28]. And

a step-up transformer is included to transform the electricity from the low voltage

machine side to the medium voltage side for inter-array collection grid.

This section directly applied the detailed model of the variable speed direct-driven

PMSG (Type 4) based wind energy generation system. The proposed modeling

approach is developed using SimPowerSystems of MATLAB/Simulink. The dynamic

performance of the proposed PMSG based wind energy generation system and

especially its harmonic emission impact is discussed and evaluated through digital

simulations carried out using detailed simulation method [26].

4.1.2 Parameter Setting of Wind Turbine

The Synchronous Generator and Full Scale Converter (Type 4) Wind Turbine Detailed

Model from Matlab example is the original fundamental of the model validation. The

main parameters of the investigated wind turbine are shown in table 4-1.

Table 4-1: Parameters for 2MW wind turbine

Rated power 2 MW Cpmax 0.46

Cut-in speed 3m/s Air density 1.225kg/m3

Rated speed 12m/s Rotor 80m

Cut-out speed 25m/s Sweep Area 5027m2

Nominal voltage 575 V Nominal DC voltage 1100V

Nominal Frequency 50Hz Line filter capacitor

(Q=50) 0.15MVar

Inertia Constant 4.32s Grid-side converter

nominal voltage 575V

Nominal DC bus voltage 1100 DC bus capacitor 90mF

Stator, rotor leakage

inductance 0.124p.u.，0.116p.u. Switching frequency 1950Hz

Stator, rotor resistance 0.024p.u.，0.0396p.u. Excitation inductance 2.9p.u.

4.1.3 Model Simulation Results

A simple wind energy conversion system is built via Matlab/Simulink. In this paper,

the base speed is considered as 15m/s. The output voltage is 575V at 50Hz. The

simulation results show the steady state performance of the PMSG-based wind energy

conversion system. The output power of the wind turbine can always approach its

optimal value, while the reactive power is kept to be close enough to zero. But

imperfect reacting time at the beginning and the harmonic issues could be observed

from the scope plot.

Fig. 4-2: Inner construction illustration of wind turbine

As shown in Figure above, after analyzing and compare the harmonic

characteristics of the machine-side converter current Iabc_stator and the grid-side

converter current Iabc_grid_conv, the result is shown below:

（a）wave form of machine-side converter current

（b）wave form of grid-side converter current

Fig. 4-3: wave form of machine-side and grid-side converter current

After the FFT analysis, the harmonic characteristics of current are shown below:

Table 4-2: Harmonic characteristics of current from machine-side and grid-side

converter

Harmonic machine-side converter grid-side converter

THD 117.32% 6.51%

3 2.08% 0.07%

5 3.84% 0.14%

7 1.16% 0.17%

9 0.75% 0.02%

11 0.66% 0.03%

13 0.31% 0.01%

Fig. 4-4: harmonic characteristics of machine-side converter current (x-axis: harmonic

frequency [Hz])

Fig. 4-5: harmonic characteristics of grid-side and grid-side converter current (x-axis:

harmonic order)

It can be deducted from the figure above that machine-side converter current

contain extremely high level of harmonics. It can be speculated that the machine-side

output current that could only be relied on wind turbine mechanical control strategy is

the main reason. The detail analysis of the reason will be left for further study in the

future. Grid-side converter current, which contains much less harmonic, is mainly

influenced by the control of converter control, from which can be seen that full scale

converter of PMSG could decrease influence of the fluctuation and mechanical

control of wind turbine to the harmonic of gird side.

From the figure 4-5, the grid-side converter current still contains a relatively high

level of 5th and 7th harmonic, after installing a 0.15MVar Line filter capacitor, the

result from comparing the current before and after the filter is shown below:

(a) Wave form of grid-side converter current before filter

(b) Wave form of grid-side converter current after filter

Fig. 4-6: Wave form of grid-side converter current before and after filter

After the FFT analysis, harmonic characteristics of grid-side converter current is

shown in table below:

Table 4-3: Harmonic characteristics of grid-side converter before and after the filter

Harmonic Before After

THD 6.51% 1.27%

3 0.07% 0.08%

5 0.14% 0.26%

7 0.17% 0.84%

9 0.02% 0.03%

11 0.03% 0.02%

13 0.01% 0.01%

(a) before the filter (b) after the filter

Fig. 4-7: Harmonic characteristics of current before and after filter

From the analysis in figure 4-7, the filter mainly filters the 5th, 7th and 9th

harmonic, etc. Furthermore, the filter is more effective to higher harmonic, thus, filter

in wind turbine out port has a significant effect in reducing the THD and increasing

the power quality.

4.1.4 Summary

Direct Drive PMSG Wind Energy Generation System is introduced in this

chapter. Based on the example from MATLAB/Simulink Synchronous Generator and

Full Scale Converter (Type 4) Wind Turbine Detailed Model, after analyzing the

harmonic characteristics of machine-side converter current, grid-side converter

current and current after line filter capacitor, it could be deducted that machine-side

converter current is mainly influenced by wind speed and mechanical control system.

Grid-side current, which has a lower harmonic to the machine-side current, are mainly

affected by PWM control system of converter. Thus, harmonic current injected from

PMSG to grid is mainly determined by gird side converter and filter in wind turbine

out port.

4.2 Offshore Wind Farm System

4.2.1 System Description

The offshore wind farm system investigated in this report get reference information

from the 300MW scale offshore wind farm, which is located in Rudong county, China,

built and operated by CHINA HUANENG company from 2015. The collection grid

layout, parameters for electric devices are mainly referred to this Rudong OWF. Only

scaling down the total capacity of the investigated wind farm to 160MV. The eight

2MW PMSGs are connected in one string type clustering. And total string number is

ten. After boosted to 33kV, the chain-linked wind turbine are connected to offshore

boost transform station through low and large capacity mid-voltage set cable. When

boosted to 230kV, AC or DC transmission strategy are adopted to reach the

gird-connection point.

（a）

（b）

Fig. 4-8: The electrical system for the HVAC (a) and VSC-HVDC (b) transmission

system of offshore wind farm

In most cases, the cable type will be a three-core, armored cable with copper or

aluminum conductors and XLPE insulation. The cable will have integrated fiber optic

unit for communication purposes.

Each WTG is rated for 2MW. Ideally assuming a power factor of 1, each WTG will

supply a current of 35A in the 33kV cable strings. The combined current of the remote

end eight turbines will be 280A. Because of the low using time of wind farm, in most

cases the current of low capacity mid-voltage set cable is lower than 280A. Hence, the

95 mm2 cross section cable is picked for the connection for the remote end eight

turbines. The maximum current of high capacity mid-voltage set cable is 560A. Hence,

the 400 mm2 cross section cable (rated current 590A) is selected for the feeder section.

The parameter comes from the user’s guide for XLPE submarine cable system from

ABB Ltd, as shown in following table.

As the table D-1 in appendix gives the parameters for 30kV three-core cables with

copper wire screen. The chosen 95 mm2 cross section cable capacitance is 0.18μF/

km and its inductance is 0.44 mH/km, resistance (maximum dc resistance at 20℃)

is 0.193 Ω/km.The chosen 400 mm2 cross section cable capacitance is 0.29μF/

km and its inductance is 0.35 mH/km, resistance is 0.0991 Ω/km. And 300 mm2

230kV submarine cable is selected as 230kV AC transmission system. Parameters of

AC 230kV submarine cable is shown in table 4-7.

Parameters of Booster Substation is shown in table 4-6. The main parameters of

Converter Station is shown in table 4-8.

Table 4-4: Parameters of Low Capacity mid-voltage set cable

Parameter Area/mm2 Resistance

Ω/km

Inductance

mH/km Capacity μF/km

Charging

current A/km

Value 95 0.193 0.44 0.18 1.0

Table 4-5: Parameters of Submarine cable (33kV high capacity mid-voltage set cable)

Parameter Area/mm2 Resistance

Ω/km

Inductance

mH/km Capacity μF/km

Charging

current A/km

Value 400 0.0991 0.35 0.29 1.6

Table 4-6: Parameters of Booster Substation

Parameter Wire winding

resistance/Ω

Eddy current loss

resistance/Ω Leakage/mH

Value 0.036 10.03 0.191

Table 4-7: Parameters of AC 230kV Undersea Cable System

Parameter Area/mm2 Resistance

Ω/km

Inductance

mH/km Capacity μF/km

Charging

current A/km

Value 300 0.00127 0.44 0.14 3.7

Table 4-8: Parameters of Converter Station

Parameter Length/km Rated

power/MW

DC

Capacity/uF

reactor

resistance/Ω

reactor

inductance/mH

Value 70 200 70 0.0251 8

4.2.2 Simulation Validation of the OWF case

Based on MATLAB/Simulink synchronous generator and full scale converter (Type

4) wind turbine detailed model, the detailed offshore wind farm model was first built

according to the OWF configuration design discussed in previous section 4.1.

However, the complexity of the control loop of converters causes the simulation

running time too long.

In the average type of Type 4 wind turbine model, the IGBT Voltage-sourced

converters (VSC) are represented by equivalent voltage sources generating the AC

voltage averaged over one cycle of the switching frequency. The average model

preserves the dynamics resulting from control system and power system interaction.

This model allows using much larger time steps (typically 50 microseconds), thus

allowing simulations of several seconds. Thus, by testing both the detailed model and

the average model of the Type 4 wind turbine, the harmonic output characteristics

from wind turbine unit has no significant difference. In the following wind farm

model building, the wind turbine will be applied in the average model, for keeping the

simulation test more efficiently.

The 160MW wind farm module in the grid-connected model includes eight rows of

wind turbines. Each row of wind turbine is composed of eight wind turbines which

are 2MW. After boosted to 33kV, the chain-linked wind turbine are connected to

offshore boost transform station through low and large capacity mid-voltage set cable.

When boosted to 230kV, AC or DC transmission strategy are adopted to reach the

gird-connection point.

VSC-HVDC is selected as one type of transmission system for this offshore wind

farm. The flexible DC transmission system studied in this paper is the VSC-HVDC

system of ±100kV, and the AC side is connected to the network of 230kV. The

schematic diagram is shown in Fig. 4-9.

Fig. 4-9: The schematic diagram of the simulation system of VSC-HVDC

The rectifier side adopts the constant active power and constant reactive power

control modes, and the inverter side adopts constant AC voltage and constant DC

voltage control modes. The structure diagram of the converter station in the system is

shown in Fig. 4-10:

Fig. 4-10: The schematic diagram of the simulation model of converter station in

flexible DC system

The transformation ratio of transformer of the converter station is 33kV/230kV, the

rated capacity is 200MW, the impedance of the primary side and the secondary side

are 0.0025+j23.55p.u. The filter at the exit is used to filter 27 to 54 harmonics with

rated power of 18MVar and 22MVar respectively. The impedance of the smoothing

reactor on the DC line is 0.0251+j2.512, and the parallel capacitance on the DC side

is 70uF.

4.2.3 Simulation Results and Analysis of Harmonic Output

Characteristics

As can be seen in previous section, the simulation system includes a large amount

of high-frequency power electronic switching elements, thus, much high harmonics

will be imported into the system. As a comparative study, the FFT bar plot of offshore

wind power grid system at PCC point are shown in the Fig. 4-11, x-axis is the

harmonic order.

Fig. 4-11: FFT bar plot of offshore wind power grid system at PCC point

The simulation model for the investigated offshore wind farm is validated. Thus the

harmonic distribution when no filter is installed at collection node could be illustrated

in the spectral diagram Figure 4-11. According to IEEE Std 519-2014, the maximum

allowable harmonic distortion level for bus with voltage over 161kV is stated. For the

odd harmonic order (h<11), THD should be less than 3.0%. While 11<h<23, THD

level should below 1.5%. And for 23<h<35, THD value needs to be smaller than

1.15%. The following figure plot the simulated THD values for the OWF compared

with the maximum allowable standard level.

Fig. 4-12: THD bar plot of current harmonics at the connection point to the onshore

As can be seen roughly in spectrum, the harmonic order mainly consists of 3, 5, 7,

9, 23, and relatively severe distortion level around the low frequency range, which

could heavily influence the voltage quality at the on-shore grind connection point.

This leads us to explore some harmonic suppression strategies, to design effective

filters that could erase most of high harmonics.

4.3 Summary

Direct Drive PMSG Wind Energy Generation System is introduced in this chapter.

Based on the example from MATLAB/Simulink Synchronous Generator and Full

Scale Converter (Type 4) Wind Turbine Detailed Model, after analyzing the harmonic

characteristics of machine-side converter current, grid-side converter current and

current after line filter capacitor, it could be deducted that machine-side converter

current has very high level harmonic distortions, due to the only mechanical control

system of the wind turbine rotor. The grid-side current, which has a lower harmonic

level, is mainly affected by advanced PWM control system of the voltage sourced

converter. Thus, harmonic current injected from PMSG to grid is mainly determined

by gird side converter and filter in wind turbine out port. The simulation model for the investigated 160MW offshore wind farm is validated.

The harmonic order mainly consists of 3, 5, 7, 9, 23, and relatively severe distortion

level around the low frequency range, which could heavily influence the voltage

quality at the on-shore grind connection point. This leads us to explore some

harmonic suppression strategies, to design effective filters that could erase most of

high harmonics.

Chapter 5 Harmonic Resonance Analysis in

OWF

5.1 Introduction

For small scale systems, the influence of harmonic impedance on the system can be

neglected. But for large-scale systems such as offshore wind farms, the existence of

harmonic impedance cannot be neglected. The AC system harmonic impedance and

the distribution of background harmonic voltage characteristic are important in the

domain of power system analysis and design. This section will focus on analyzing the

characteristic of harmonic impedance in network components of electric transmission

capacitor, discussed the resonance and harmonic current amplification, which may be

caused by cables.

Resonance frequency is an important part of harmonic analysis of offshore wind

farm. Frequency domain analysis is often used in harmonic resonance analysis. The

harmonic resonance problem in OWF requires consideration of the topology of the

offshore wind farm collection system. Furthermore, the complexity of the collection

grid increases the difficulty of harmonic resonance analysis.

The occurrence of resonance will seriously endanger the safety and stability of the

system operation. In this section, the system resonance problem will be analyzed by

building the harmonic model of offshore wind farm installation, simulating the system,

and then the frequency scan method is applied to detect the influence components

which potentially affect the harmonic resonance.

5.2 Theory of Harmonic Models

In order to analyze the harmonic generation mechanism of the wind power field

accurately, harmonic models of each component in the OWF installation which are

suitable for harmonic analysis should be established. Harmonic models are often

linearized in frequency domain analysis.

5.2.1 Harmonic Model of PMSG with full scale converter

This kind of wind power system uses the multi-poles permanent magnet alternator,

therefore the wind turbine and the generator does not need to install the speed gearbox,

becomes the direct driven turbine generators, as shown in Fig. 5-1. The inverter

connects the stator windings of the generator with the power grid, and converts the

frequency-changing energy into constant-frequency power with the same frequency as

the power grid. Because of the decoupling control of the inverter, the variable-speed

wind turbine based on synchronous generator is completely decoupled from the power

system, and its characteristics depend entirely on the control strategy of the inverter.

At the same time, because the inverter is at the stator side, all the power emitted by

the generator needs to be transformed by the inverter, and the capacity requirement of

the inverter is increased significantly for the large capacity wind power system. The

advantage of this kind of wind turbine is to omit the lift speed gearbox, to avoid the

maintenance and replacement of gear box parts, to improve the stability of the system

structure and to enhance the reliability.

GridG

WindBlade

Direct-driven Wind

Turbine Generators

LS

AC/DC DC/AC

Boosting transformer

Fig. 5-1: Direct-driven variable speed wind turbine based on permanent magnet

synchronous generator

Characteristics of direct-driven permanent magnet synchronous wind power

system:(1) The permanent magnet generator has the highest operating efficiency; (2)

The excitation of permanent magnet generator is not adjustable, which leads to the

change of induction electromotive force with speed and load [52]. With controllable

PWM rectifier connecting with DC/AC transform, the DC bus voltage is basically

constant and the electromagnetic torque of the generator can be controlled to adjust

the speed of the wind wheel; (3) High cost of permanent magnet generator and

full-capacity full-control converter; (5) The permanent magnet generator has the

locating torque, which is difficult to start the unit.

The power path of direct drive PMSG consists of two parts, the rectifier and the

inverter. The operation flow is that: generators emit low-frequency alternating current

and becomes DC after rectifier, The DC power passes through the large capacitance

filter as the input end of the inverter. The control signal obtained by the power

network is transformed to obtain the AC power which can be connected to the grid

operation.

The influence of harmonics generated by wind turbines on the power grid is mainly

reflected in the grid-side converter of the PMSG. In this section, the grid-side

converter is further analyzed on the basis of many research, and the corresponding

harmonic model is established according to the harmonic characteristics [53]. This

chapter will not go into those details.

High Frequency Harmonic Model

For the grid-side converter, the control strategy can use sinusoidal pulse width

modulation (SPWM), space vector pulse width modulation (SVPWM) and so on. The

output voltage harmonics is relative to the control strategy that converter applied.

There are quite a lot existing literature discussing the harmonic voltage expression

under different control methods. Here limited to the direction and length of this thesis,

the discussion will not be listed in details. The harmonic output voltage expression

under SVPWM control strategy is given directly:

0 0

0 0 0 0 / 3

an a n

n a b c

U U U

U U U U

(5-3)

In which, 𝑈𝑛0 is the neutral point voltage of the load to the DC capacitor.

𝑈𝑎0, 𝑈𝑏0, 𝑈𝑐0 is the three-phase voltage of abc phases.

In normal working condition, the amplitude of the grid-side converter output

harmonic is constant. Therefore, grid-side converter in high frequency section could

be equivalent to an independent harmonic voltage source. The high frequency

harmonic model including L type filter is shown in Fig. 5.2. In which, 𝑈ℎ is the

equivalent harmonic voltage source in high frequency section.

L R

hU

Fig. 5-2: High frequency harmonic model of grid-side converter including L filter

If the grid-side converter contains a LCL filter, the high frequency harmonic model

can be equivalent to Fig. 5.3:

hU

1L2L

fC

sR

Fig. 5-3: High frequency harmonic model of grid-side converter including LCL filter

Among them, 𝑈ℎ is the equivalent harmonic voltage source for high frequency

range, 𝐶𝑓 is the filter capacitor, 𝑅𝑠 is the damping resistor, 𝐿1 and 𝐿2 are filter

inductors.

Low frequency harmonic model

The harmonic characteristics in low frequency range of the grid-side converter is

affected by the controller. The output of the phase voltage is also affected by the grid

voltage. The harmonic output voltage of the grid-side converter exhibits controlled

characteristics. Thus, low frequency harmonic output could be represented by

independent controlled voltage source. The derivation of harmonic voltage and wave

impedance is quite complex, and the formulas are shown as follows:

1

bridge

op

v

UU h

C h

(5-4)

1

1

L

eq

v

C h Z hZ h

C h

(5-5)

Of which 𝑈𝑏𝑟𝑖𝑑𝑔𝑒 is the extra harmonic from the nonideal state of the component

and 𝐶1(ℎ), 𝐶𝑣(ℎ) is the transfer function of the feed-forward current loop or voltage

loop.

As can be seen above, the low frequency harmonic model of grid-side converter

can be equivalent to Fig. 5.4:

opU h

eqZ h

Fig. 5-4: Low frequency harmonic model of grid-side converter

5.2.2 Harmonic Model of Transformer

Offshore wind farms are collected by many wind turbines through the collection

grid. And the power is fed to the onshore grid, which contains more transformers

during the transmission of power. The transformers can be roughly divided into two

kinds. One is the step-up transformer installed on the output of the single wind

generator. The other one is step-up transformer on the substation in the sea before

high voltage power transmission system. In order to analyze the harmonic of offshore

wind farm, an appropriate harmonic model should be set up for the transformers in

wind farm.

At present, there already exist many kinds of harmonic models for transformers.

Under the condition of power frequency, the influence of excitation branch will not be

considered. But when the frequency changes, the influence of excitation branch and

the skin effect of windings cannot be ignored. It is generally believed that the Model 6

is relatively closer to the actual reality in the common harmonic analysis frequency

band. Thus, it is commonly accepted that the Model 6 is more accurate harmonic

model of transformer. Model 6 (CIGRE model) equations are listed as following:

, 1 0 t a nt a n

Ts p T

XR R X

(5-11)

20.693 0.769ln 0.042 ln

tanS S

e

(5-12)

2

2

1

tan 10 tan1 /10 tan

p T T TT s T

p T

jR X X h XZ h R jhX

R jX h

(5-13)

Where 𝑅𝑠, 𝑅𝑇 is the resistance and eddy current loss of wire winding respectively.

Both of them do not change with frequency; S is rated power of the transformer.

The model assumes that the eddy current loss is proportional to the square of

frequency, and to consider the demagnetization effect in the case of lower frequency,

which can well reflect the working condition of the transformer, and will get higher

accuracy in the harmonic analysis. The equivalent harmonic model structure can be

seen in Fig. 5.5:

pRsR

TjhX

Fig. 5-5: Equivalent circuit for harmonic model of transformer

5.2.3 Harmonic Model of Subsea Cables

Offshore wind farms are integrated by a lot of wind turbines through collection grid

and are usually far away from the coast. As a result, a large number of cables with

different voltage levels are used in the process of power transmission.

Power cable is different from conventional transmission line, and its distribution

capacitance parameter is larger, which will have a great influence on the harmonic

resonance of offshore wind farm, such as amplification on harmonic currents. Thus, it

is necessary to establish harmonic model of offshore power cables, which will make

results of harmonic analysis of OWF more accurate.

Usually, the unit length of submarine cable can be equivalent to a lumped

parameter π-equivalent model. But when the length of submarine cable reaches a

critical point, considering the long-term effects of submarine cables, a lumped

parameter π-equivalent model cannot reflect the influence of skin effect, and thus

requires the use of multiple π-equivalent circuit cascades or distributed parameter

model.

The π-equivalent circuit is shown as follows:

LZ h

2

LY h 2

LY h

Fig. 5-6: Equivalent circuit for harmonic model of submarine cable

The parameters of the equivalent circuit can be calculated by the following formulas:

L L LZ h R jhX (5-14)

LY h jhB (5-15)

When the voltage level is 220kV and above, the equivalent circuit resistance can be

calculated by the following formula:

0.74 0.267 1.073L LR h R h (5-16)

When the voltage level is below 220kV, the equivalent circuit resistance can be

calculated as below:

0.187 0.532L LR h R h (5-17)

5.2.4 Harmonic Model of VSC- HVDC system

A complete VSC-HVDC system consists of a converter transformer, a converter

station and a DC line. The station at the sending end works in the rectifier mode,

while the station at the receiving end works in the inverter mode [52]. Taking the

two-terminal flexible DC transmission system as an example, the system diagram is

shown in Fig. 5.7.

DC cableAC system

US UC

Convertor station A

Convertor station B

Fig. 5-7: The diagram of the two-terminal flexible DC transmission system

The flexible DC transmission system can adjust the amplitude of the converter

output voltage and the power angle of between the converter output voltage and

system voltage by turning on and off power electronic devices so as to independently

control the active power and reactive power output.

Considering the assumption of the high symmetry and independent of the two sides

of the VSC-HVDC system, the complete system can be represented as two

independent systems. Considering the characteristics that the secondary side uses the

connection mode ′∆′ and zero sequence current can not flow in the system, one

side of the single line structure of VSC-HVDC can be further simplified as the

following circuit.

Fig. 5-8: The structure of three-phase VSC

According to the simplified principle and content, if there is no special explanation

in the paper, the one-side system of VSC-HVDC is generally used for analysis.

The high frequency mathematic model based on switching transfer functions

By using the Kirchhoff voltage law, the voltage of the A phase in Fig. 5.8 can be

written to satisfy the equation:

𝐿 (𝑑𝑖𝑠𝑎

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑎 = 𝑢𝑠𝑎 − (𝑢𝐴𝑁 + 𝑢𝑁𝑂) (5-18)

It can be assumed that the switching function of the upper arm of the A phase is

Sa , and the switch function of the lower bridge arm is Sa′ . The switching function S

only takes 0 and 1 , 0 represents disconnection, and 1 represents conduction. When

Sa=1、Sa′=0 , that is, the upper arm of the A phase is connected, and the lower bridge

arm is disconnected, which means uAN=ud . When Sa=0、Sa′=1 , that is, the upper

arm of the A phase is disconnected, and the lower bridge arm is connected, which

means uAN=0 . Considering that the upper and lower bridge arms can not be

switched on or off simultaneously, the switching function must satisfy Sa + Sa′=1. By

substituting it into the formula (2.6), it can be get that

𝐿 (𝑑𝑖𝑠𝑎

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑎 = 𝑢𝑠𝑎 − (𝑆𝑎 ∙ 𝑢𝑑 + 𝑢𝑁𝑂) (5-19)

Similarly, the voltage equations for the B and C phases are as follows:

𝐿 (𝑑𝑖𝑠𝑏

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑏 = 𝑢𝑠𝑏 − (𝑆𝑏 ∙ 𝑢𝑑 + 𝑢𝑁𝑂) (5-20)

𝐿 (𝑑𝑖𝑠𝑐

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑐 = 𝑢𝑠𝑐 − (𝑆𝑐 ∙ 𝑢𝑑 + 𝑢𝑁𝑂) (5-21)

Considering the characteristics of the three-phase three-wire system, 𝑖𝑠𝑎 + 𝑖𝑠𝑏 +

𝑖𝑠𝑐 = 0. When the voltage of each phase of three-phase AC system is balanced, 𝑢𝑠𝑎 +

𝑢𝑠𝑏 + 𝑢𝑠𝑐 = 0. By substituting it into the formula (5.19~5.21), it can be get that [52]

𝐿 (𝑑𝑖𝑠𝑎

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑎 = 𝑢𝑠𝑎 − 𝑢𝑑 ∙ (2𝑆𝑎 − 𝑆𝑏 − 𝑆𝑐)/3 (5-22)

𝐿 (𝑑𝑖𝑠𝑏

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑏 = 𝑢𝑠𝑏 − 𝑢𝑑 ∙ (2𝑆𝑏 − 𝑆𝑎 − 𝑆𝑐)/3 (5-23)

𝐿 (𝑑𝑖𝑠𝑐

𝑑𝑡) + 𝑅 ∙ 𝑖𝑠𝑐 = 𝑢𝑠𝑐 − 𝑢𝑑 ∙ (2𝑆𝑐 − 𝑆𝑏 − 𝑆𝑎)/3 (5-24)

The differential equations of the DC side can be written as follows:

𝐶𝑑𝑢𝑑

𝑑𝑡= (𝑆𝑎 ∙ 𝑖𝑠𝑎 + 𝑆𝑏 ∙ 𝑖𝑠𝑏 + 𝑆𝑐 ∙ 𝑖𝑠𝑐) − 𝑖𝑑 = 𝑖𝑑𝑐 − 𝑖𝑑 (5-25)

The high frequency mathematical model of VSC is composed of the above four

equations. From the expression of the mathematical model, it can be seen that the DC

side current in the rectifier or inverter side is determined by the three phases of the

switching function, so the switching function belongs to a nonlinear and time-varying

mutual coupling system. According to the mathematical model of VSC, the circuit of

the VSC in the three-phase stationary coordinate can be equivalent. The DC side and

the AC side are equivalent to two independent networks, and the AC side is equivalent

to a three-phase controlled voltage source [53], [54]. The DC side is equivalent to a

controlled current source, and the AC and DC side are coupled with each other by

means of VCCS and CCCS. The characteristic also makes the VSC-HVDC system

convenient to form parallel and multi terminal system expediently.

The low frequency dynamic model of VSC-HVDC

As mentioned earlier, the high frequency mathematical model of VSC-HVDC is

relatively accurate to describe the switching process of the converter station, but it is

difficult to be used for the controller design. The optimization of controller link in

VSC-HVDC system plays an important role in improving system reliability and

flexibility. In order to establish a mathematical model of a flexible HVDC system

with controller design, the switching action need to be simplified, and the main

simplification is to ignore the harmonic components produced during the

commutation process. According to the formula (5-22~5-24), the low frequency

dynamic model of VSC in three phase stationary coordinate system can be obtained:

{

𝐿 ∙ 𝑑𝑖𝑠𝑎 𝑑𝑡⁄ + 𝑅 ∙ 𝑖𝑠𝑎 = 𝑢𝑠𝑎 − 𝑣𝑎𝐿 ∙ 𝑑𝑖𝑠𝑏 𝑑𝑡⁄ + 𝑅 ∙ 𝑖𝑠𝑏 = 𝑢𝑠𝑏 − 𝑣𝑏𝐿 ∙ 𝑑𝑖𝑠𝑐 𝑑𝑡⁄ + 𝑅 ∙ 𝑖𝑠𝑐 = 𝑢𝑠𝑐 − 𝑣𝑐

𝐶 ∙ 𝑑𝑢𝑑 𝑑𝑡⁄ = 𝑖𝑑𝑐 − 𝑖𝑑

(5-26)

In the three-phase stationary coordinate system, the mathematical model of

VSC-HVDC can clearly and simply represent the principle and operation process of

the system. Then harmonic model of VSC-HVDC converter is similar to grid-side

converter of PMSG [55].

5.3 Developing the Equivalent Harmonic Model of the OWF

The theory fundamentals are described in the last section. Therefore, the simplified

equivalent harmonic model of the investigated OWF could be validated step by step.

PMSG with full scale converter

The influence of harmonics generated by wind turbines on the power grid is mainly

reflected in the grid-side converter of the PMSG. As previous description, the

grid-side converter could be equivalent to an independent harmonic voltage source.

Fig. 5-9: Equivalent circuit for harmonic model of PMSG grid-side converter

Transformer

Fig. 5-10: Equivalent circuit for harmonic model of transformer

Subsea Cables

Fig. 5-11: Equivalent circuit for harmonic model of submarine cable

VSC- HVDC transmission system

In the three-phase stationary coordinate system, the mathematical model of

VSC-HVDC can clearly and simply represent the principle and operation process of

the system. Then harmonic model of of VSC-HVDC converter is similar to grid-side

converter of PMSG

Fig. 5-12: Equivalent circuit for harmonic model of VSC-HVDC grid-side converter

HVAC transmission system

HVAC transmission system can be treated as a AC cable, thus the equivalent circuit

similar to the subsea cables. The onshore grid can be seen as an ideal voltage source.

Fig. 5-13: Equivalent circuit for harmonic model of HVAC transmission system and

the onshore grid

Establish the equivalent circuit for harmonic model of OWF in MATLAB/Simulink

based on the parameters above, and each low capacity mid-voltage cable is 1km, large

capacity mid-voltage cable is 3km and high voltage cable is 50km, capacity of shunt

reactor installed in PCC point of AC transmission system is 200Mvar. The parameters

list is shown in table 5.8, which are converted to 230kV. The equivalent circuit models

of OWF with HVAC and HVDC transmission system are shown in appendix fig. A.2

and A.3.

Table 5-1: Offshore wind turbine harmonic model parameters

element symbol value

LCL filter

Grid-side inductance Lf1 428.59mH

Converter-side

inductance Lf2 850.79mH

Capacity Cf1 0.028uF

Wind-turbine

transformer

(0.575/33kV)

Wire winding

resistance Rs1 3.137Ω

Eddy current loss

resistance Rp1 11393Ω

Leakage Lt1 189.6mH

Small capacity

medium pressure set

cable

Resistance Rcable1 0.294Ω/km

Inductance Lcable1 0.647mH/km

Capacity Ccable1 0.247uF/km

Large capacity

medium pressure set

cable

Resistance Rcable2 0.11Ω/km

Inductance Lcable2 0.752mH/km

Capacity Ccable2 0.728uF/km

Off-shore booster

main transformer

(33/230kV)

Wire winding

resistance Rs2 1.76Ω

Eddy current loss

resistance Rp2 487.02Ω

Leakage Lt2 29.37mH

230kV High voltage

cable

Resistance Rcable3 0.00194Ω/km

Inductance Lcable3 0.44mH/km

Capacity Ccable3 0.14uF/km

5.4 Results and Harmonic Resonance Analysis

Frequency scan method was used to find the resonant frequency and frequency

impedance for those equivalent circuit models. Variable-controlling approach is

expounded and applied in the following analysis. There are two factors that may

influence the resonance phenomenon.

1) The transmission system selected: HVAC or VSC-HVDC.

2) The submarine cable parameters, including the length, inductance and

capacitance.

5.4.1 The Influence of Transmission System on Harmonic

Resonance in OWF

For HVAC transmission system there are three main resonant frequency at collection

grid bus of wind farm: 33Hz, 148Hz and 313Hz as shown in fig 5-14, where the

resonant resistance are 8.2Ω, 43Ω and 380Ω. When system is operated under such

frequency, the resonance will bring influence to the power quality grid-connection.

Fig. 5-14: Harmonic Impedance of Offshore Wind Farms with HVAC transmission

system

From figure 5-15, in HVDC transmission system, resonance frequency is 310Hz,

similar to HVAC system. The resonant resistance is 407Ω, larger than HVAC

transmission system.

The main resonance frequencies are similar at collection grid bus of wind farm in HVAC

transmission system and HVDC transmission system, which are between 6 and 7

frequency order.

Fig. 5-15: Comparison between HVAC and HVDC Harmonic Model of Offshore

Wind Farms

5.4.2 The Influence of Cable on Harmonic Resonance in OWF

Submarine cables contain a lot of distributed capacitance and inductance. Those

nonlinear elements will aggravate the harmonic current distortion and distortion rate.

More than that, those capacitive elements from cable are very likely interacted with

those inductive elements, such as wind turbine windings etc., which then resulting in a

resonance circuit, triggering resonance, and endangering the security of the collection

grid system. Resonance phenomenon could not only make the electric equipment in

the system run abnormally, but also endanger the safety and stable operation of

offshore wind farm.

The selection index of a cable can be its cable length, inductance and capacitance

value. In this section, three factors from cables that may affect harmonic resonance of

wind farm collection grid are simulated and analyzed by Simulink through the

impedance scanning method.

Variable-controlling approach is expounded and applied in the following analysis.

It means that when looking at the effect of one variable, all other variable predictors

are held constant in order to assess or clarify the relationship between the investigated

variable and the target result. And how to apply this approach in solving the influence

of cable parameters (cable length, inductance and capacitance) will be indicated in

below sections in details.

1) The influence of cable length

The length of the cable laid in the offshore wind farm depends on the location of

the wind turbines and the distance between the wind turbine export and the grid

connection point. The cable lengths required by different wind turbine units are also

different. Due to the influence of laying length, the number of capacitor and

inductance leaded in from the marine cable is different, and the electrical parameters

will also change accordingly. Therefore, the harmonics generated in offshore the wind

farm will vary greatly. It is of great significance to study the different effects of the

same type of cable with different lengths on the resonance point in wind farm.

Select the same model cable (such as 33kV cable shown in table 5.4) of different

length of 3m, 5km, 7km and 9km, respectively. Record the harmonic frequency at the

grid connection point.

From Fig. 5-16, the longer distance of cable laid, the lower resonance frequency

happened, and the impedance of the cable at resonance point will slowly increase.

Fig. 5-16: Frequency characteristics of cable impedance with different lengths

The increasing of the cable length leaded in a growth of the distributed capacitance,

and the increasing the capacitance value. Therefore, the frequency of resonance,

which happened with the inductive element in the system, is shifted to a lower

direction.

2) The influence of cable inductance

When studying on the influence of cable inductance on resonance problem, the

system is equipped with the same length and the same capacitance value of the cable,

changing the inductance value of the cable, then analyze the Simulink simulation

results. The formula for the inductance of a cable is shown below：

1 12

L LX XL

f (5-27)

Where 𝑓1 is the fundamental frequency, and 𝑋𝐿 is positive sequence reactance of

the system.

Here 4 kinds of cables are selected. And their inductance parameters are 0.6mH/km,

0.52mH/km, 0.45mH/km and 0.32mH/km respectively. They have same length of

3km, the capacitance value of 0.29μF/km, and the positive sequence reactance value

is 0.0991Ω/km. Simulation analysis is carried out, and the simulation results are

shown in Fig. 5-17.

Fig. 5-17 (a) Frequency characteristics of cable impedance with different inductances

Fig. 5-17 (b) Frequency characteristics of cable impedance with different inductances

(detail)

With the gradually increasing of cable inductance, the frequency of resonance will

move to a lower frequency accordingly, while the resonant impedance will increase.

Therefore, in the design and construction progress of a new offshore wind farm,

selecting the reasonable inductance values of the laying cables should be based on the

harmonic compatibility test results. At the same time, harmonic adaptability test can

also offer reasonable data support and advice for designing proper filters at the later

stage.

3) The influence of cable capacitance

Both the length and the inductance value of cable will affect the harmonic

resonance characteristics of offshore wind power system. In addition, cable

capacitance will also influence the harmonic resonance characteristics, because

submarine cables contain a large number of distributed capacitance. The cable with

the same length and inductance value is adopted, and the submarine cable with

different capacitance is selected to be simulated.

The capacitance values of the 4 cables selected are0.15μF/km ,0.20μF/km ,

0.25μF/km, 0.3μF/km respectively. The cable length is 3km, the inductance value is

0.32mH/km , and the positive sequence reactance value is 0.0991Ω/km .The

simulation result is shown in Fig. 5-18.

Fig. 5-18(a) Frequency characteristics of cable impedance with different capacitances

Fig. 5-18(b) Frequency characteristics of cable impedance with different capacitance

values (detail)

From above figures, under the variable-controlling approach, the increasing of

capacitance can cause the system resonance frequency shift to lower frequency, and

resonant impedance increases at the same time.

5.5 Summary

The occurrence of resonance will seriously endanger the safety and stability of the

system operation. In this chapter, the system resonance problem is analyzed by

building the harmonic model of offshore wind farm installation, simulating the system

in equivalent circuit. And then the frequency scan method is applied to detect the

influence components which potentially affect the harmonic resonance. Harmonic

distortion measured at the WTG terminals is dependent on the network to which it is

connected [51]. From the simulation results, the main resonance points are similar at

collection grid bus of wind farm in HVAC transmission system and HVDC

transmission system, which are around 7th order. Resonance points are also influenced

by length, inductance and capacitance of submarine cable, due to the high distributed

capacitance of submarine cable. It was shown in chapter 4 that PMSG can generate

appreciable level of low order harmonics which are close to resonance point of

collection grid in offshore wind farm, so some harmonic suppression strategies should

be found.

Chapter 6 Filter Design for Suppressing

Harmonics in OWF

6.1 Introduction

Comparing to onshore wind turbine generators, offshore direct-driven PMSG wind

turbines have a relatively larger scale and a more complicated construction. Upon

multiple wind turbine generators operated in parallel, harmonics amplification occurs

easily. This phenomenon exacerbates the harmonics and results in serious voltage

distortion that may even exceed the grid limit. In the meantime, a massive

implementation of subsea cable and high-power electronic devices greatly increases

the number of capacitance and inductance, which is a directly cause of harmonics

issue. Therefore, the strategy for suppressing the harmonics at offshore wind farm has

become one of the hardest subjects in this field.

Distorted voltage and current cause abnormal operating conditions in a power

system. The unwanted harmonics are generated by nonlinear loads, which are loads

implemented with semiconductor devices and/or iron-cored devices. Such loads are

the power supplies, UPS, motor drive systems, transformers, electronic ballast,

electronic appliances, rectifiers, and any other power electronics circuits.

To reduce or eliminate the unwanted harmonic components in a power system,

previous researchers have come up with solutions to harmonics issue from several

perspectives. One is to introduce filters, including passive filters, active power filters

and hybrid filters [56]. The hybrid filters all try to achieve a high performance in the

elimination of harmonics while minimizing the costs by combining an active and a

passive filter. Any detailed classification of the hybrid filters is out of the scope of this

thesis. Based on the current application of filters, the design of one typical type of

passive filters and the active power filter (APF) is stated and simulated at the

investigated offshore wind farm for suppressing harmonics. Filters can be designed

and applied to the system in order to meet better voltage quality requirements.

Besides design of filter, optimization of network structure is another harmonic

suppression strategy worth considering. Considering the potential harmonic resonance

in advance, the reasonable cable selection and collection grid layout and configuration

of system provides better harmonic feature.

6.2 Passive Filter

6.2.1 Fundamental of passive filter

The passive filters are realized with LC components, and active filters are realized

using different types of inverter topologies. The filter parameters are set through

calculation. The resistance at resonance frequency can be effectively damped by

passive filter. The impact caused by harmonics is then reduced, protecting grid from

harmonic pollution. Compared to active filter, passive filter has a larger capacitance,

fits for higher voltage and well compensates reactive power. Therefore passive filter is

widely implemented in wind farms.

According to working principle and structure, passive filters can be roughly sorted

as single turned filters, dual turned filters, second-order high pass filters, C-type high

pass filters, etc. Their basic components are shown in figure 6-1 as follows.

Fig. 6-1: Five common passive filters [57]

a. Single turned filter

Single turned filter is made of a simple serially connected resistance, capacitance

and inductance. The cost of single turned filter manufacture and installation is

relatively lower. However, subjected to its simple structure, single turned filter only

eliminates or suppresses harmonics that occurs at a specific design frequency. The

harmonics occurs at other random frequencies cannot be effectively dealt with.

Besides, the power consumption of filter increases as higher order harmonics occurs,

essentially leads to its low economic performance.

b. Dual turned filter

Differ from single turned filter, dual turned filter has another resistance and

inductance in parallel and connected to single turned filter. Dual turned filter

suppresses or eliminates harmonics occurs at two design frequencies. Dual turned

filter is able to suppress harmonics at two frequencies, one of the harmonic circuit

bears lower voltage. The cost of dual turned filter is therefore lower than two single

turned filter, and the installation is simpler as well. Thus dual turned filter is an

optimum choice for offshore wind farm.

c. Second-order high pass filter

Second-order high pass filter is consisted of a capacitance and a serial connected

resistance and inductance. It is usually used to absorb harmonics of multiple orders.

The capacitance usage rate of second-order high pass filter is relatively high, but its

capability on specific frequency is worse than single turned filter [58]. With a damper

configured, on the other hand, the power consumption is reduced, enhancing the

a b e c d

system stability. Therefore second-order high pass filter is widely installed and

implemented.

d. Third-order high pass filter

Third-order high pass filter has a capacitance connected with a resistance in series.

This capacitance is smaller than the capacitance in the major line, but the resistance at

fundamental frequency can be effectively increased.

e. C-type high pass filter

Based on second-order filter, C-type filter installs another capacitance, which

reduces fundamental harmonic loss and provides certain amount of reactive power

compensation.

Other than the advantages and positive features mentioned above, passive filters

exhibits also following disadvantages.

(1) Subjected to the filter features, individual parameter configuration fits only for

specific harmonics. Once the system harmonic shifts, previous filter configurations

are not applicable. The flexibility and compatibility of passive filter is therefore worse

than active filter, it behaves a high reliance on system configuration.

(2) Filter performance is highly subjected to its parameter setting. The harmonic shifts

and residual resistance usually leads to unpreventable gap from its ideal performance.

(3) Passive filters are commonly connected with system resistance in series or in

parallel and produce harmonics. This harmonics may burn the filter itself and even

leads to a series grid accidents.

6.2.2 Design theory of C-type high-pass filter

Due to a massive use of large-scale electronic devices, a large amount of high-order

harmonic exists in offshore wind farms. Besides, low-order harmonics are also

produced by wind turbine units and the whole wind farm collection grid. Both

harmonics endanger severely system stability and economic operation.

C-type high pass filter is effective on suppressing high-order harmonics and also

removing harmonic resonance at indicated frequencies. The diagram of C-type filter

structure is shown in Fig. 6-2. The damping resistance R is directly connected with

the series shunt L-𝐶1 in order to reduce the fundamental energy loss of the filter [59].

Fig. 6-2: The circuit diagram for C-type high pass filter

The total impedance of the filter is:

1 1

1

2 2

2 2

2 2 2 2

( ) ( )( )

( ) ( )

L C L C

C

L C L C

X X X XZ R j R X

R X X R X X

(6-1)

The impedance modulus is:

2 1 1 1

2 2

2 2 2 2

2 2 2 2

( ) ( )

( ) ( )

L C C C L C

L C L C

R X X X X X XZ

R X X R X X

(6-2)

According to the above equations, at fundamental frequency, when the inductance

L and the capacitance𝐶2 together generates the series resonance, there is no

fundamental power loss at the resistance R and the loss only exists in the harmonic

current. Besides, 𝐶1 can be treated as the system voltage support to generate reactive

power at the fundamental voltage. Its capacitance value is decided by the required

system reactive power [60, 61].

The system rated power angular frequency is 𝜔1. Limit the L and 𝐶2 to fullfill：

1

2

1=

LC (6-3)

When harmonic resonance occurs:

2 1

0L C CX X X (6-4)

Then the frequency of nth-order harmonics is:

1 2

1 2

n

C C

LC C

(6-5)

For this nth-order harmonic, the C-type filter can be equivalent to a RC circuit

connected in series, where the filter impedance reaches down to the minimum [62].

The number of major harmonics that needs to be filtered should be set at that point.

According to equation (6-3) and (6-5):

𝑛𝐷= 2

1 1

1n C

C

(6-6)

According to equation (6-6), the minimum impedance of C-type filter depends on

the ratio of 𝐶2 over 𝐶1. When the specific order 𝑛𝐷 of harmonics that needs to be

eliminated is known, the capacitance of 𝐶2 and 𝐶1 could be obtained by calculation.

Then the characteristic equation of filter is obtained as:

min

2 2 2 2 2 2 2 2

1 1 1 1

1

1 1

Z

R n C R n C R

(6-7)

By analyzing and calculating the characteristic equation, the minimum resonance

impedance can be adjusted to ensure the safe and stable operation of the filter.

6.2.3 Parameter design of C-type high-pass filter

In order to study the filtering effect of C-type high-pass filter, this section aims to

design a proper filter and analyze the harmonics before and after the filter installed in

the investigated offshore wind farm system.

From chapter 4, the simulation model for the investigated offshore wind farm is

validated. Thus the harmonic distribution when no filter is installed at collection node

could be illustrated in the spectral diagram. According to IEEE Std 519-2014, the

maximum allowable harmonic distortion level for bus with voltage over 161kV is

stated. For the odd harmonic order (h<11), THD should be less than 3.0%. While

11<h<23, THD level should below 1.5%. And for 23<h<35, THD value needs to be

smaller than 1.15%. The following figure plot the simulated THD values for the OWF

compared with the maximum allowable standard level.

Fig. 6-3: Spectral diagram of current harmonics at PCC without filters

Table 6-1: Simulated system specification

Voltage of the AC network (kV) 230

Frequency (Hz) 50

Fundamental-Freq. Short-circuit reactance (W) 1

dc-side voltage of HVDC converter (kV) ±100

Based on the previous design equations, we could follow the blow steps to design

and calculate the parameters of C-type filter [59-62].

1) The target harmonic order that needs to be eliminated is 𝑛𝐷. In the investigated

wind farm model, the target elimination order of harmonics located at 5th order,

7th order and 9th order. Set 𝑛𝐷 = 9. From equation (6-6), the ratio of 𝐶2 over 𝐶1

is calculated to be 80.

2) The reactive power demanded by an HVDC converter is often expressed in terms

of the dc-side power [59]. Based on the reactive power required to compensate the

power factor at fundamental frequency, only 𝐶1 could supply reactive power at

fundamental frequency:

Q𝐶1 = U2𝜔1𝐶1 (6-8)

Assume the Q𝐶1 is 25MVar, then the capacitance 𝐶1 is 1.5μF.

3) Based on the design value of ratio 𝑛𝐷 and 𝐶1 , the value of 𝐶2 could be

calculated as

𝐶2 = 𝐶1(𝑛𝐷2 − 1) (6-9)

Then the capacitance in the series branch 𝐶2 is 120μF.

4) Based on the limiting condition that

1

2

1=

LC (6-10)

The parameter value of inductance L could be set down.

𝐿 =1

𝜔12∙𝐶2

= 84.4mH (6-11)

5) Combined considering of the request of the filtering effect and the system

impedance parameter, the first step is to determine the minimum impedance of the

filter. The minimum impedance value of the designed filter is assumed to be 1.

And then according to formula (6-12) to find the R value,

𝑍𝑚𝑖𝑛 ≈1

𝑛𝐷2𝜔1

2∙𝐶22𝑅

(6-12)

The shunt resistance of the C-type filter is 8.68Ω.

Here should note that, when R increases, 𝑍𝑚𝑖𝑛 decreases, but in higher harmonic

regions, 𝑍𝑚𝑖𝑛 curve will increase in amplitude [63]. Therefore, in determining

the resistance R value, not only should consider 𝑍𝑚𝑖𝑛, but also take into account

the impedance requirements of the entire frequency section.

6) The capacity of capacitance 𝐶2 in the series branch could be calculated as

Q𝐶2 = Q𝐶1𝐶1

𝐶2 (6-13)

Above all, the design of the C-type filter is realized step by step. Its reactive power

compensation capacity is 25MVar. The target harmonic order that needs to be

eliminated is set to 9th order. Then parameters of C-type filter can be calculated by

equations (6-6) to (6-12). The shunt resistance of the C-type filter is 8.68Ω, the

inductance is 84.4mH, the capacitance is 1.5μF, and the capacitance in the series

branch is 120μF.

6.2.4 Results analysis

The C type filter is inserted at the grid-connected point, and the model is run on the

simulation platform. The model diagram of the model accessing the filter and the

topology of the filter are shown in the following figure 6-4.

Fig. 6-4: The model of wind farm with the C-type filter

The simulation model of C-type filter established in Matlab is shown as Fig. 6-5.

Fig. 6-5: The simulation model of C-type high pass filter

The harmonic spectrum analysis diagram without and with the filter are shown in

the following figure. As can be seen from the diagram, the main harmonics in this

OWF system are odd order harmonics, especially in the low order range, in which the

higher harmonic components are the 5th, 7th, 9th and the 11th order harmonics. And

the phenomenon that relatively large THD values at 23rd and 25th order harmonics is

also worth to mention. It acts coordinated with the previous chapter 5, which did

impedance scanning on the whole system. The x-axis is the harmonic order.

Without the access of filter With the access of C-type filter

Fig. 6-6: The harmonic spectrum analysis diagram without and with the C-type filter

From the above spectrum analysis diagram, the total harmonic distortion of current

at the grid-connected point is reduced from 7.71% to 0.64%. And the THD values for

the low order harmonic are also less than 0.2%, which means the designed filter can

weaken the low frequency range of harmonics effectively. The grid-connected current

approximates the sine wave reasonably with very high power quality, and the

grid-connected point harmonic level meets the requirements of relevant specifications.

Fig. 6-7: The harmonic spectrum analysis diagram before and after the access of

C-type filter

6.3 Active power filter

6.3.1 Fundamental of active power filter

Nowadays, active power filters (APF) are the only solution which is able to

improve power quality in contemporary power systems with distributed generation

and dynamical changes of supplying current and voltage distortions [64]. The inner

power source is the main difference between APF and passive filter. Introducing APF

is a compensation for the shortage of passive filter.

Many researchers put a lot attention on APF recent years. Japan has realized APF

essentially application, not only on improving harmonic features, but on improving

the grid quality compensation. Europe has also put a lot resources on APF research,

and some of the offshore wind farm has already introduced APF in their harmonics

suppression strategies.

The active filter can be connected in parallel or in series with the load. The main

idea of their operation is that they inject currents that are contrary to the harmonics of

phase with fundamental currents. In this way they eliminate harmonic fundamental

currents. Compared with passive filter, active filter has better performance. It has the

advantage of programming to block multiple harmonics rather than just one harmonic.

They can also provide reactive power when needed, and can also compensate for

neutral currents. A large number of harmonic components can be eliminated by the

same filter. In addition, active filters do not have the risk of resonance with other

network components like passive filters. The cost of high power rated converters is

the biggest drawback of active filters, even though prices are falling. The design of

APF is more complicated and may cost higher power losses with lower reliability.

And it can handle lower power compared to the conventional passive filters.

The basic working principle of an active converter works is illustrated in the

following diagram. As seen 𝑒𝑠 is the AC supply. According to Fig. 6-8, an active

power filter consists of 2 part: one is command current operational circuit, the other is

compensate current generation circuit. A compensating circuit is made up of a current

control tracking circuit, a drive circuit and a main circuit. The main function of

operational circuit is to detect the harmonic component at compensating current,

while the major function of compensating circuit is to generate proper compensating

current according to the operation result [67]. More detail fundamentals about APF

model are listed at appendix.

Fig. 6-8: Working principle of a basic APF

6.3.2 Design of LCL active filter

The LCL filter is a new type of active grid-connected filter in recent years, which

impedance is inversely proportional to the frequency of the current. Therefore, the

suppression of higher order harmonics is more prominent than that of conventional

passive filter and it can be well applied to harmonic suppression of the offshore wind

farm [66]. The schematic diagram of active filter is shown in the following figure.

The Fan Side The Grid Side

Fig. 6-9: The schematic diagram of active filter

The LCL filter consists of a DC module, an AC module and a power switch module.

The fan side of the filter is composed of the resistor 𝑅1 and the inductor 𝐿1, and the

grid-side is composed of the resistor 𝑅2 and the inductor 𝐿2. There is a capacitor 𝐶𝑓

with a Y-shaped connection between the two sides. The inductor 𝐿1 is used to

suppress harmonics of low orders, and the inductance 𝐿2 and capacitor 𝐶𝑓 are used

to suppress harmonics of high orders as well as improve the stability of the power grid

[66]. The overview diagram of structure of LCL APF is shown below.

Fig. 6-10: Overview diagram of the LCL active filter [66]

The basic principle of LCL filter is that inductors show low impedance

characteristics and capacitor shows high impedance characteristics at low frequency,

thus current at fundamental frequency will go through inductors to grid; At high

frequency, capacitor has low impedance and inductors shows high impedance, so high

frequency harmonics will be filtered out through capacitor. Compared to L filter, LCL

filter achieves a higher attenuation with limited values of inductors and capacitors.

In practical applications, large-scale offshore wind farms have a number of wind

turbines. Therefore, in order to avoid the resonant oscillation of the LCL filter, it is

usually added damping. The LCL filter with damping can also effectively reduce the

energy consumption of passive damping and improve the working precision and

efficiency of the filter. According to the regulation, the voltage on the inductor is 10%

less than the effective value of the system line voltages. This paper takes a ripple

current of 20%, and the formula is written as

1

1

0.28

dcN

s

UI

f L

(6-14)

In the formula, Udc is the system bus voltage, fs is PMW switch frequency, I1N

is the equipment rated current.

For converter side inductance L1, the constraint is

2

1

1

3

2

dc m

m

U UL

f I

(6-15)

In the formula, f1 is the fundamental frequency, Um is the peak of the phase

voltage of the power grid, Im is the peak of the phase current of the power grid.

Because of the limitation of the filter power factor, in order to prevent the reactive

power output of the filter from increasing indefinitely, the reactive power of the LCL

filter is set to 95% of the rated capacity of the converter, which is written as

2

1

(1 95%)6

Nf

N

PC

f U

(6-16)

Finally, the damping coefficients are set, as follows:

2

1 1 22 ( )

cf fK L C

L L L

(6-17)

In this way, we can calculate the parameters of the LCL with the active damping

filter in the VSC grid-connected mode to achieve the suppression of harmonic

resonance.

From equations (6-14) to (6-17), parameters of LCL APF can be set:

1) For 1L ，set 0.636 ≤ 𝐿1 ≤ 2.198𝑚𝐻，to reduce the weight ,volume and building

cost , 𝐿1 = 2𝑚𝐻 is selected.

2) For fC ，assume Q = 0.01 NP ，then

𝐶𝑓 =0.01𝑃𝑁6𝜋𝑓1𝑈𝑁

2 = 28.34𝜇𝐹

𝐶𝑓 = 30𝜇𝐹 is selected to sample the calculation.

(3) Set damping coefficients ξ=8%，then 𝐿2 = 1𝑚𝐻 is selected.

6.3.3 Results analysis

The LCL filter is inserted at the grid-connected point in the simulation model with

APF in series. The model diagram of APF for detecting the harmonic component at

compensating current and the configuration of the LCL filter are shown in the

following figures.

Fig. 6-11: Model diagram of APF’s access

Fig. 6-12: Configuration of the LCL filter

Without the access of filter With the access of the LCL active filter

Fig. 6-13: The harmonic spectrum diagram without and with the LCL active filter

Harmonic spectrum with the designed LCL active power filter are shown in Fig.

6-13. The total harmonic distortion of current at the grid-connected point is reduced

from 7.71% to 4.68%. And the low order harmonics are all suppressed below 0.5%.

The result can meet the IEEE harmonic standard. The THD bar plot of the

investigated system without and with the designed LCL active filter is drawn as in Fig.

6-14.

Fig. 6-14: The THD bar plot of the system without and with the LCL active filter

In this work simulation, the direct use of APF in series installed at the end of the

VSC-HVDC grid-side converter station. The results for system with the designed APF

seem not to be as satisfying as for the system with passive C-type filter. It could be

concluded that APF is also a feasible solution for reducing the overall THD level for

the OWF system. However, due to the limitation of research and understanding of the

design of APF, this thesis work didn’t get very persuasive results after the access of

the designed LCL type APF. It still need further investigation in the future work.

Now APF is a mature technology with low pressure and small capacity, while the

high voltage and large capacity APF is not mature. And the effect of LCL active filter

is not very satisfied due to its expensive investment for electronic equipment,

especially in large scale offshore wind farm. After further research, the passive filters

are the most common and better strategy for the converter station. In addition, the

parallel type APF is mainly used in industry, but the series APF is not so commonly

applied.

6.4 Summary

Several methods for harmonics suppression are performed in this chapter. Passive

filters, active power filters are introduced respectively. Time-domain based simulation

methods of offshore wind farm and filters are built in MATLAB/Simulink. The

harmonics distribution in cases with C-type filter or active power filter adopted are

designed and analyzed with simulation models. Through the simulation case study

above, a passive filter with C-type filter combined performed a satisfying results on

harmonics suppression, the harmonic distortion of current of the grid-connected point

is reduced from 7.71% to 0.64%. And the THD values for the low order harmonic are

also less than 0.2%, which means the designed filter can weaken the low frequency

range of harmonics effectively. An active power filter solution has also been designed

and analysis, however the effect is not very satisfied. The harmonic distortion of

current of the grid-connected point is reduced from 7.71% to 4.68%. In future work,

further study on APF design and the optimal parameters of hybrid filters will be

chased to improve harmonics suppression.

Chapter 7 Conclusion

7.1 Conclusion

In this thesis work, a comprehensive harmonic analysis in offshore wind farm was

studied. Firstly, the fundamental of the offshore wind farm installation and basics of

harmonic are described. Secondly, a suitable model of one offshore wind farm is

built and validated in Simulink, based on the type 4 wind turbine example and

VSC-HVDC transmission system example in MATLAB. Moreover, the equivalent

circuit is calculated for the components in the aggregated wind farm based on their

harmonic model. And then the resonance problems are analyzed by frequency scan

method to calculate the potential resonance impedance and frequency. As well, the

two types of transmission system and the cable parameter selection are simulated to

evaluate the various influence on the resonance issue. Afterwards, based on the

self-built system model, potential harmonic issues that arise in the system are

investigated in time domain to interpret the THD at PCC between the OWF

collection grid and the onshore grid. At last, a C-type filter and an LCL active power

filter are designed and performed a satisfying results on harmonics suppression.

1) Simulation models of offshore wind farm system is established. The harmonic

current injected from PMSG to grid is mainly determined by gird side converter and

filter in wind turbine out port. The harmonics are mainly influenced by the converter

control strategy and switching frequency of electronic devices. Only some relatively

high emission occurs at higher harmonic orders, which is lack of enough power to

influence the voltage quality of the whole grid system, and for other frequencies

where the distortion levels are traditionally lower. The overall THD level of

harmonic output from wind energy generation system is relatively small.

2) System resonance problem of OWF was analyzed in equivalent circuit models.

And then the frequency scan method is applied to detect the influence components

which potentially affect the harmonic resonance. From the simulation results, the

main resonance points are similar at collection grid bus of wind farm in transmission

system of HVAC and VSC-HVDC, which are both around 7th order. Resonance

points are also influenced by length, inductance and capacitance of submarine cable,

due to the high distributed capacitance of submarine cable.

3) Time-domain based simulation of offshore wind farm and filters are built in

MATLAB/Simulink. The harmonics distribution in cases with C-type filter and

active power filter adopted are designed and analyzed in simulation models. A

passive filter with C-type filter combined performed a satisfying results on

harmonics suppression. The designed LCL active power filter has also been proved

to be effective on filtering the harmonics, but not very suitable for such large scale

capacity system.

7.2 Future Work

This project is just a simple trial to build the large scale offshore wind farm model

in numerical simulation software. To pursue the possible factors resulting in

harmonic and resonance issues in the collection grid, various cases are performed in

Matlab/Simulink. There are quite a lot shortages and interest points that may

promote future work.

In this work, the harmonics analysis only focus at the grid connected terminal

with considering of power quality to the onshore grid. However, the harmonics

not only affect the power grid, but also can affect the HVDC transmission

system. This direction is another interesting research scope which may be for

further work.

Due to large cable system involved, it is important that switching over-voltage is

considered, and appropriate over-voltage protection is needed for the collection

grid design [68].

The modeling of harmonic propagation and damping is still a very difficult

subject. This may not be a serious research challenge by itself. Estimating

harmonic voltage and current levels remains a serious challenge when there is

limited amount of network or component data available. Detailed models exist

but are often not applicable due to lack of data [69].

Due to the limitation of this research and understanding of the design of APF,

this thesis work didn’t get very persuasive results after the access of the

designed LCL type APF. It still need further investigation in the future work.

For the harmonic suppression strategy, the combination application of the active

filter and passive filter has not been considered in this paper. Only the single

type filter is studied and simulated. Further study of the combination of the two

filter strategy helps to make up for the shortcomings of a single type filter and to

eliminate harmonics more effectively.

Appendix

A. Offshore Wind Farm Test Case

（a）

（b）

Fig. A-1: The electrical system for the HVAC (a) and HVDC (b) connection of the

160 MW offshore wind farm

Fig. A-2: harmonic model of HVAC transmission system in OWF

Fig. A-3: harmonic model of HVAC transmission system in OWF

Wind

turbine

Transformer Cable

Grid

High

voltage

cabel

B. Mathematical model of APF in ip-iq detection algorithm

ip-iq algorithm is deducted from the basis of H.Akagi’s instantaneous power theory.

The algorithm is able to measure the harmonic current and voltage precisely when

grid voltage is asymmetry.

Take voltage vector u and it’s vertical direction vector as a basis of phasor,

orthogonal decompose the current vector i on the basis, define the ip, current in the

direction of u, as the instantaneous active current in three-phase circuit, and the iq,

current in the vertical direction of u, as the instantaneous reactive current in

three-phase circuit, ip, iq are expressed as below:

p = cosi i (B-1)

q = sini i (B-2)

Vector diagram between ip, iq, u and i in α-β coordinate system is shown in fig.E-1.

α

u

uα

i

iα

uβ

β

iβ

φu

φi

φ

ip

iq

Fig. B-1: Vector diagram between ip, iq in α-β coordinate system

p

q

sin( ) -cos( )u u=

-cos( ) -sin( )-

u u

uui i iwt wt

i ii u wt wtu

(B-3)

ip-iq harmonic detection principle block diagram is shown in Fig. B-2, The

phase-locked loop is used to determine the frequency of the a-phase voltage to get

the positive sequence voltage phasors, harmonic command current are named after

iab,ibb icb. After multiplied by matrix C32, three phase current are transformed to iα and

iβ, which are ip and iq after multiplied by matrix C. After the low pass filter process,

DC component corresponding to the three-phase current in the fundamental current,

pi and qi , can be deducted. Subtracting the fundamental current with the

compensated three-phase load current is the final harmonic command current.

iα

iβ

ip

iq

ia

ib

ic

ip

iq

iαf

iβf

iaf

ibf

icf

iah

ibh

ich

ua

PLL

LPF

LPFC32 C C23C

sin(wt)

-cos(wt)

Fig. B-2: ip-iq harmonic detection schematic

Where

T

23 32C C (B-4)

sin( ) -cos( )C=

-cos( ) -sin( )

wt wt

wt wt

(B-5)

C. Control modes adopted in the converter station

The main control modes adopted in the converter station include voltage amplitude

control and power angle control:

(1) The bus voltage amplitude control in wind farms

In the d-q synchronous rotating coordinate system, the shaft d is positioned on

the wind farm bus voltage vector SU . It can be get that

cos

sin

dS d q

q

q d

diL U U Ri Li

dt

diL U Ri Li

dt

（C-1）

Assume that the converter output voltage amplitude U remains unchanged,

0U=U , when d qi i， and produce a small disturbance at the point of

operation, the linearization and Laplace transform are applied to them in the neglect

of disturbance of angular frequency. It can be get that

0 00 2 2

0 00 2 2

cos ( )sin

( ) ( )

sin ( )cos

( ) ( )

d

q

L sL Ri U

sL R L

L sL Ri U

sL R L

（C-2）

The instantaneous power disturbance is that

0 0

0 0

T T

d d d d

q q q q

I U U iP=

I U U i

（C-3）

By means of necessary calculation and simplification, the linearized transfer function

between active power and power angle can be obtained, additional high-pass filter is

added in the control to effectively suppress resonance. The magnitude of the output

AC voltage of the converter U is controlled as

0 ( )

( ) / ( )

U=U G s I

G s Ks s

（C-4）

In the formula (C-4), ( )G s is the high-pass filter, I is current. After applying

the control, the linearized transfer function between the active power and the power

angle is

2

2 2( ( )) ( )

as bs cP=

sL R G s L

（C-5）

In the formula (C-5),

2

0 0 0 0

2

0 0 0 0

0 0 0 0 0 0

( cos )

( )( cos )

cos [ ( )] sin

S

S

S S

La U U U

R G sb U U U

c U U R G s U U

（C-6）

In order to keep the bus voltage of the wind farm stable, the voltage amplitude

controller shown in Fig. C-1 is used. srefU is the reference value of the bus voltage

and 0refU is the reference value of the convert output voltage.

Fig. C-1: The AC voltage amplitude controller (AVAC)

According to the formula (C-4) in the above control principle, the component of

d-q axis of the output voltage of the converter is controlled by the following

formulas:

0d d

q q

U =U G(s)i

U G(s)i

（C-7）

(2) The power angle control

The phase difference between the bus voltage of the wind farm and the output

voltage of the converter is the power angle. When the wind farm is connected to grid

through the AC / DC hybrid transmission system, the VSC-HVDC must adopt the

constant active power control, and the fluctuation of the wind power will lead to the

change of the power in the AC transmission line. The active power control(APC)

shown in Fig. F-2 is adopted in order to maintain the constant power control of the

VSC-HVDC when the power flow changes.

Fig. C-2: The active power controller

The angle deviation can be get after integrating the deviation between the active

power reference value refP and the transmission power of VSC-HVDC VSCP . With

the reference of the given frequency of the controller's built-in clock 0f and phase

02 f t , the d-axis orientation position of the converter output voltage and the

angle of Park inverse transformation can be get by shifting angle. The d-axis

orientation position is shown as Fig. C-3.

Fig. C-3: The d-axis orientation position

Therefore, the angle deviation will be adjusted to change the relative position of the

d-q axis orientation by the integral link when there is a deviation between the

transmission active power and the given value. In essence, the power angle is

adjusted so that the VSC-HVDC transmission power is kept at a given reference

value and the constant active power control is realized.

When the grid-connected wind farm is purely flexible, the voltage of the wind farm

is kept stable by the amplitude controller, and the frequency of the wind farm is

controlled by the built-in clock of the controller. According to the above active

power control link, it can be get that

0

( )[ ]

2

ref VSCK P P= t=2 f t

（C-8）

In the formula (C-8), the frequency of the wind farm is adjusted as follows.

0

( )

2

ref VSCK P Pf f

（C-9）

Therefore, the wind farm bus is controlled as a power point whose voltage amplitude

is stable and the frequency is f , which realizes the synchronous transmission of

wind power.

Due to the fluctuation of wind power, there is a deviation between the given

reference value of active power refP and the transmission power VSCP . According

to the formula (C-9), the deviation between the frequency of the wind farm and

built-in clock frequency of the given controller will exist because of the fluctuation

of wind power. The reference value of active power refPis generally given according

to the average output of the wind farm, so the deviation between refP and the

real-time output of the wind farm.is less. Therefore, when the wind farm output

changes, the frequency of wind farm f will fluctuate in the range of allowable

deviation of the frequency 0f .

D. Subsea cable parameters from ABB

Table D-1: Parameters for 30kV three-core cables with copper wire screen

Cross

section

of

conduc

tor

Diamet

er of

conduc

tor

Insulati

on

thickne

ss

Diamet

er over

insulati

on

Cross

section

of

screen

Outer

diamet

er of

cable

Cable

weight(

Alumi-

num)

Cable

weight(

Copper

)

Capacit

ance

Chargi

ng

current

per

phase

at 50hz

Inducta

nce

mm2 mm mm mm mm2 mm kg/m kg/m uf/km A/km mH/km

Three-core cables, nominal voltage 30kV(Um=36kV)

70 9.6 8.0 28.0 16 100.6 16.9 18.2 0.16 0.9 0.46

95 11.2 8.0 29.6 16 104.0 17.7 19.5 0.18 1.0 0.44

120 12.6 8.0 31.0 16 107.0 18.4 20.7 0.19 1.0 0.42

150 14.2 8.0 32.6 16 110.5 19.3 22.1 0.21 1.1 0.41

185 15.8 8.0 34.2 16 114.0 20.1 23.6 0.22 1.2 0.39

240 18.1 8.0 36.5 16 118.9 21.4 25.9 0.24 1.3 0.38

300 20.4 8.0 38.8 16 123.9 22.6 28.2 0.26 1.4 0.36

400 23.2 8.0 41.6 16 123.9 24.6 32.0 0.29 1.6 0.35

500 26.2 8.0 45.0 16 137.3 26.7 36.0 0.32 1.7 0.34

630 29.8 8.0 48.6 16 145.1 29.2 40.9 0.35 1.9 0.32

800 33.7 8.0 52.5 16 154.4 32.2 47.2 0.38 2.1 0.31

Table D-2: 10-90kV XLPE 3-core cables

10-90kV XLPE 3-core cables

Cross section mm2

Copper conductor Aluminum conductor

A A

95 300 235

120 340 265

150 375 300

185 420 335

240 480 385

300 530 430

400 590 485

500 655 540

630 715 600

800 775 660

1000 825 720

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